Jaime Harrison, the Democrat challenging Senator Lindsey Graham of South Carolina, raised an astonishing $57 million from July through September, the highest quarterly fund-raising total for any Senate candidate in U.S. history and part of a flood of Democratic money remaking the battle for control of the Senate.

From South Carolina to Maine to Arizona, anger at President Trump and his Republican allies has fueled a steady flow of cash to Democratic challengers all year. But Senate Republicans’ pledge to quickly replace Justice Ruth Bader Ginsburg on the Supreme Court, despite their blockade of President Barack Obama’s nominee in 2016, has enraged the Democratic base, and donations have surged to extraordinary levels.

Mr. Harrison’s fund-raising haul heightens the stakes of the Supreme Court confirmation hearings that Mr. Graham will begin overseeing on Monday as the chairman of the Senate Judiciary Committee, as Republicans rush to seat Judge Amy Coney Barrett, Mr. Trump’s nominee, before the election.

Across the map, the Republican Party is mounting expensive defenses of seats it once thought were safe, stretching its resources to hold on to a Senate majority that it hopes will check the power of Joseph R. Biden Jr., the Democratic presidential nominee, if he wins in November. Polls show Mr. Biden with a consistent lead, and Republicans are growing increasingly worried about the possibility of unified Democratic control of Washington in 2021.

“We saw this in 2018 when a green wave translated into a blue wave,” said Brian Walsh, a former communications director for the National Republican Senatorial Committee. “We’ll know in November if it’s going to repeat itself.”

Democrats must win four Republican-held Senate seats to take the majority, or three if Mr. Biden wins the White House, as the vice president serves as the tiebreaker. Democratic strategists widely expect to lose one seat in Alabama, but the party is competitive in races for close to a dozen Republican-held seats.

Money, of course, does not guarantee victory, and Mr. Graham is still running in a conservative state that has not sent a Democrat to the Senate in more than two decades. Recent polls have shown a dead heat: In a Quinnipiac University survey late last month, Mr. Graham and Mr. Harrison were tied at 48 percent, with 95 percent of likely voters saying their minds were made up.

Republican leaders had hoped that the chance to fill a Supreme Court seat, which has historically motivated Republican voters more than Democrats, would provide a crucial late boost and draw attention away from the Trump administration’s mishandling of the coronavirus pandemic.

Instead, Democrats have seen an explosion of voter energy in response to the prospect of a conservative Supreme Court majority that could overturn Roe v. Wade and block liberal policies for a generation. At one point shortly after Justice Ginsburg’s death was announced last month, the Democratic donation platform ActBlue was processing more than $100,000 every minute.

Mr. Harrison did not so much break a fund-raising record as shatter it: Before this year, the biggest quarterly haul for a Senate candidate was $38 million, raised by former Representative Beto O’Rourke of Texas during his unsuccessful challenge to Senator Ted Cruz in 2018. Mr. Harrison blew past that by nearly $20 million, raising more than twice as much in a single quarter as Mr. Graham reported raising in the previous six quarters combined. (Mr. Graham has not yet announced his third-quarter numbers.)

ImageMr. Graham still has a good chance of winning in South Carolina, with recent polls showing him and Mr. Harrison in a dead heat.
Credit…Anna Moneymaker for The New York Times

“Not even Jaime could have predicted this level of enthusiasm and financial support,” said Clay Middleton, a Democratic National Committee member from South Carolina who is advising the Harrison campaign.

The campaign received 1.5 million donations from 994,000 donors, according to Mr. Harrison’s campaign, and the average contribution was $37.

But much of the money came from out-of-state donors, which raises questions about how much it reflects the sentiments of South Carolina voters versus the feelings of the national electorate.

Mr. Graham’s reversal on seating a Supreme Court justice in an election year has enraged liberal donors nationally, said Curtis Loftis, the Republican state treasurer, but not necessarily as many voters in South Carolina.

“I don’t think he’ll pay a penalty for that all,” Mr. Loftis said. “We don’t hold politicians in such high regard here. We don’t believe everything they say.”

Mr. Graham caused another stir at a candidate forum on Friday when he declared that Black people “can go anywhere in this state” as long as they are “conservative, not liberal.” Critics quickly called out Mr. Graham, who is white, for what they described as an attempt to dictate an acceptable path for Black political leaders while debating Mr. Harrison, who is Black, in a state with a long and troubled racial history.

Mr. Harrison will have the money to amplify that or any other past Graham comments. On a drive Mr. Loftis made last week from Columbia to Charleston, the Harrison campaign “owned every billboard from here to there,” he said. But given the state’s conservative bent, he added, “I’m not sure money can take Jaime over the top.”

Still, the fact that the race is competitive at all speaks to the intense energy among Democrats, and to how Republican worries about a challenging year have turned into fears of a national landslide. South Carolina, which voted for Mr. Trump in 2016 by more than 14 points, has not elected any Democrat statewide since 2006 and has not sent a Democrat to the Senate since 1998, when Ernest F. Hollings was re-elected.

Mr. Harrison’s huge fund-raising total also speaks to Democratic voters’ specific anger at Mr. Graham, who has become one of Mr. Trump’s most vocal defenders and, as chairman of the Senate Judiciary Committee, is leading the charge to confirm Judge Barrett.

Mr. Harrison has been campaigning heavily across the state, including in “deep Republican areas that Democrats usually write off,” said Tameika Isaac Devine, a Democrat who serves on the Columbia City Council.

And, flush with cash, Mr. Harrison has been able to blanket the state with advertising.

“You cannot turn on your TV and not see Jaime, you cannot go on the internet and not see Jaime, you cannot open your mailbox and not see Jaime,” said State Senator Dick A. Harpootlian, a Democrat who represents the Columbia area.

Mr. Harpootlian, a former chairman of the South Carolina Democratic Party, said he voted for Mr. Graham six years ago because the senator was then a bipartisan moderate.

“The word ‘bipartisan’ wouldn’t cross his lips today,” Mr. Harpootlian said, noting that Mr. Graham had flipped not only on filling the Supreme Court seat but also on Mr. Trump’s fitness for the presidency, which Mr. Graham colorfully questioned in 2015 during his own brief presidential run.

It is not clear how much of an electoral impact the biggest issues dominating national discussions — the coronavirus and the economy — will have on the race. South Carolina has recovered about half of its job losses, but the unemployment rate is still nearly double its pre-pandemic level of 3.2 percent. And while infection numbers have declined from a July peak, the state is still reporting, on average, more than 800 new cases a day.

While Mr. Graham has been a particular target, the surge in donations to Democrats extends far beyond South Carolina.

Theresa Greenfield, who is challenging Senator Joni Ernst of Iowa, reported raising $28.7 million in the third quarter, a record for a Senate candidate in Iowa. In his race against Senator Cory Gardner of Colorado, John Hickenlooper raised $22.6 million, more than four times his total in the previous quarter. And in North Carolina, Senator Thom Tillis’s challenger, Cal Cunningham, reported a record $28.3 million, though he faces a late-breaking scandal over romantic texts he sent to a woman who is not his wife.

And some of the most prolific Democratic fund-raisers in previous quarters — namely Amy McGrath in Kentucky and Mark Kelly in Arizona — have yet to announce their third-quarter numbers. Public disclosures are required later this week.

While the Supreme Court fight has mobilized Democratic donors, strategists in both parties also expect it to further polarize the electorate, which could help Republicans like Mr. Graham who are running in states where Mr. Trump is expected to prevail.

Mr. Walsh, the Republican strategist, said the Republican Party was worried that Democrats might be able to outpace it with waves of small donations well after 2020.

“There is a question not just this cycle, but cycles beyond, that Republicans are going to need to do more to compete online with small donors,” Mr. Walsh said.

The money raised by Mr. Harrison has helped push the South Carolina race — which was considered a second-tier contest, at best, at the beginning of the cycle — into the tossup category, where the nonpartisan Cook Political Report put it last week.

“Even Democrats in and outside of the Palmetto State are surprised such a typically red state is truly in play,” wrote Jessica Taylor, the Cook Political Report’s Senate analyst.

In a potential setback for Mr. Harrison, the Supreme Court recently sided with Republicans in mostly reinstating a state law that requires absentee ballots be accompanied by a witness’s signature. Democratic groups had sued to block the requirement; Trav Robertson, the state Democratic Party chairman, said South Carolina and other Southern states had originally introduced witness signatures to “prevent white people from helping African-Americans to cast their votes.”

Still, Mr. Graham himself has been sounding the alarm on Mr. Harrison’s financial advantage, going on Fox News and begging viewers for donations.

“Help me,” he pleaded on Sean Hannity’s program late last month. “They’re killing me moneywise. Help me.”