Postal slowdowns and warnings of delayed mail-in ballots are causing election officials to rethink vote-by-mail strategies, with some states seeking to bypass the post office with ballot drop boxes, drive-through drop-offs or expanded in-person voting options, despite the coronavirus pandemic.

The 2020 election was supposed to be the largest-ever experiment in voting by mail, but the Trump administration’s late cost-cutting push at the Postal Service has shaken the confidence of voters and Democratic officials alike. The images of sorting machines being removed from postal facilities, mailboxes uprooted or bolted shut on city streets, and packages piling up at mail facilities have sparked anger and deep worry.

Even if, as the Postal Service says, it has plenty of capacity to process mail-in ballots, the fear is that the psychological damage is already done. So as Democrats in Washington fight to restore Postal Service funding, election officials around the country are looking for a Plan B.

“The office has been flooded with calls for the past few days,” said Katie Hobbs, the secretary of state of Arizona and a Democrat. “The concern I have is that, like any campaign of misinformation, it attempts to undermine voters’ confidence in our process.”

Planning in the states proceeded Monday, as House Democrats prepared for a Saturday vote on legislation that would reverse cost-cutting measures at the Postal Service and pump $25 billion in emergency funding into the ailing agency. Democrats were also pressuring the Postal Service board to reverse those policies.

Postmaster General Louis DeJoy, along with Robert Duncan, the chairman of the agency’s board of governors, agreed to testify before the House Oversight and Reform Committee next week, as questions arose about a potential conflict of interest from a logistics company Mr. DeJoy holds a stake in that could be shaping the decisions of the Postal Service’s Trump-appointed leadership.

It was still unclear whether Senate Republicans would follow the Democrats’ lead and do anything that the president opposes. But endangered Republicans running for re-election were clearly feeling the heat, not from Democrats in Washington but from angry constituents awaiting delivery of medicines, supplies and other packages that they have come to rely on the post office to deliver.

The newest front in the battle over voting in 2020 is the drop box, where ballots mailed out to voters can be returned without fear of Postal Service backlogs or coronavirus infection. Once voters deposit their ballots in such boxes, they are collected by election officials and brought to polling places for tabulation.

Election officials in Connecticut, Virginia, Pennsylvania and elsewhere are seeking to expand drop-off locations for absentee and mail-in ballots, but they have met vehement opposition from President Trump and his campaign.

After spending weeks floating unsupported allegations that voting by mail would “rig” the election, the president on Monday turned to drop boxes: “Some states use ‘drop boxes’ for the collection of Universal Mail-In Ballots. So who is going to ‘collect’ the Ballots, and what might be done to them prior to tabulation?” he asked on Twitter. “A Rigged Election? So bad for our Country.”

Speaking to reporters at the White House on Monday, Mr. Trump said he wanted to “make sure that the election is not stolen, and so does everybody else.”

Drop-box expansion has so far fallen along party lines. In New Jersey, which has a Democratic governor and state legislature, state officials announced on Friday that at least 105 more drop boxes would be added across the state for the general election. In Ohio, the Republican secretary of state has said he is unable to allow for more than one drop-off location per county.

But even in Louisiana, where the Republican secretary of state on Monday sought to limit vote-by-mail options, he proposed curbside drop-off options for absentee ballots.

Beyond the drop boxes, the upheaval over the postal system is forcing many campaigns and state parties to begin their get-out-the-vote operations months earlier than expected. Susan Swecker, the chairwoman of the Democratic Party of Virginia, said the state party’s two-week get-out-the-vote program was “now a two-and-a-half-month” get-out-the-vote program.

She said the party was now encouraging municipalities to open more in-person satellite locations for the state’s 45-day early voting window, and to have far more drop boxes, which would require “an urgent push.”

“I don’t think there are enough drop boxes,” Ms. Swecker said. “That’s kind of a new thing for us around here.”

The Trump campaign has moved to counter. In Pennsylvania, where mail ballot drop boxes were widely used for the first time in the June primary, the Trump campaign is suing to block them in November. The suit, filed in June, claims that drop boxes “exponentially enhanced” the threat of fraud and don’t allow for poll watchers to monitor them.

Pennsylvanians became eligible this year to request “no-excuse” absentee ballots under a law passed by the Republican-led legislature and signed by the Democratic governor. Such ballots can be requested regardless of whether a voter is out of town, sick, or otherwise unable to go to a polling place. The pandemic drove an enormous surge in mail voting; when election officials were overwhelmed, about 20 county election boards introduced the drop boxes to ease the burden.

But the Trump campaign and Republican supporters in the state have echoed the president’s baseless attacks on mail ballots. Use of the drop boxes, the lawsuit claims, “provides fraudsters an easy opportunity to engage in ballot harvesting, manipulate or destroy ballots, manufacture duplicitous votes, and sow chaos.”

Last week, a federal judge ordered the Trump campaign to produce any evidence it has of voting fraud occurring through the use of drop boxes.

ImageNearly 90 percent of the ballots in this year’s primary came through the mail or drop-off locations in Arizona.
Credit…Adriana Zehbrauskas for The New York Times

Undeterred, the Trump campaign and the Republican National Committee announced Monday night that they would intervene in two other lawsuits, brought by the Ohio Democratic Party and the League of Women Voters, against Ohio’s Republican secretary of state to loosen rules on absentee ballot applications.

In Louisiana, the secretary of state moved to roll back vote-by-mail rules for the state’s primary. The state, which does not have no-excuse absentee ballots, had expanded who was able to vote absentee in the primary. But on Monday, the secretary of state proposed restricting the criteria for additional permissible vote-by-mail excuses to only those who have tested positive for the virus.

The plan would still have to pass the Republican legislature and be signed by a Democratic governor.

In Ohio, Frank LaRose, the Republican secretary of state, said he did not have the legal authority to unilaterally expand drop-box locations. He has since decreed that there can be no more than one drop-off location per county.

In an interview, he said that he supported drop boxes as an alternative to the mail service, but that he did not have the authority under current state law to install them.

“I would love for the General Assembly to authorize the addition of more drop boxes,” he said. “But for me to just unilaterally say, ‘Go ahead, boards of elections, install as many of these as you want’ would be irresponsible, because what I’m doing now is setting up dozens of my boards of elections for all kinds of litigation and creating the potential for more voter confusion, which is the last thing we need right now.”

Instead, he said, the state will begin a public relations campaign to get voters to mail in their ballots early. Ohio has also urged the Postal Service to move some of its processing into the state from a Detroit processing plant to cut down on delays. And it has designed its ballot envelopes with a bold-colored stripe to make sure they are visible during the sorting process.

David Pepper, the chairman of the Ohio Democrats, however, said Mr. LaRose had “spent the last month doing everything he could to stop drop boxes, delaying it for almost a month, and then unilaterally only saying one per county without a legal opinion.”

Mr. Pepper said the state Democratic Party would encourage voters, particularly if they are looking to return their ballots close to November, to use the lone drop-off site in their county.

“We will make it painfully clear where that drop box is to every voter,” Mr. Pepper said. “I want to have a 30-day parade of cars going to that one location.”

Some Democrats said on Monday they remained confident in the Postal Service to successfully process a large vote-by-mail election.

“The U.S.P.S. is set up to deal with surges all the time,” said Luke Warford, the director of voter expansion at the Texas Democratic Party, which is sticking to its vote-by-mail push. “There’s surges before elections. There’s particular surges before Christmas.”

Mr. Warford said the state party had just mailed 818,000 absentee ballot applications to eligible seniors in Texas (another state that does not offer no-excuse absentee ballots). But the ballot chase program — calling, texting and following up with those older voters to return their ballot — will begin earlier than normal this year.

In Arizona, where nearly 90 percent of the ballots in this year’s primary came through the mail or drop-off locations, the secretary of state’s office has revised its guidance for ballot deadlines, encouraging voters to mail ballots no later than Oct. 27 to ensure they arrive on time. Ms. Hobbs, the secretary of state, is also looking at other methods of returning ballots.

“We are also working with counties to increase the number of secure drop-boxes across our state, and reminding voters that they can always skip ahead at any voting location to drop off a ballot-by-mail, and some counties are providing drive-through ballot drop-off at voting locations,” Ms. Hobbs said.

Other states that are almost entirely vote by mail have had to drastically increase their voter education program. In Washington, the secretary of state’s office will be using social media and radio ads for the month leading up to the election to help inform concerned voters.

“Some voters have been upset, and we’re just trying to counter the messaging they’re hearing with the facts,” said Kim Wyman, the Republican secretary of state. “That was actually part of our plan when we started ramping up for 2020. We figured it would be foreign interference that would be ramping up disinformation; shows you what we knew.”