The spectre of Donald Trump’s imminent declaration of a new White House run looms over races in several key states ahead of Tuesday’s US midterm elections, with the former president poised to seize on any success for ultra-conservative candidates as validation for his 2024 campaign.

Opinion polls appearing to reflect a last-minute surge of support for Trump-endorsed nominees in a number of crucial congressional and governors’ contests came as the former president appeared at a rally for the Republican senator Marco Rubio in Florida on Sunday.

Heaping praise on “an incredible slate of true Maga warriors”, Trump cited his “Make America Great Again” political slogan.

Some of his preferred extremists, including Kari Lake in Arizona, Herschel Walker in Georgia and JD Vance in Ohio, have erased Democratic leads to reach election day as favorites, according to the polling website FiveThirtyEight.

Other Trumpist Republicans who once trailed by double digits, including the Senate candidates Mehmet Oz in Pennsylvania and Blake Masters in Arizona, have closed to within touching distance, giving their party hope of recapturing the chamber and providing Trump a significant lift as he prepares to declare his third run for the Republican presidential nomination.

“If this is a big night for Republicans, and they think it’s going to be, that will be a major, major victory for Donald Trump and his followers will be greatly energized,” David Gergen, a White House adviser to four presidents, told CNN.

“If they come up with anything like that kind of victory, if they turn two or three of the seats in the Senate, they control the House, it’s going to be hard to stop Trump within the Republican party. He will be, in effect, the very likely nominee.”

Most of the so-called Maga candidates have amplified Trump’s lie that his 2020 defeat by Joe Biden was the result of electoral fraud. A Washington Post analysis last month found that 291 Republican nominees in Senate, House or statewide races, more than half of those running, have denied or questioned Trump’s defeat.

Democrats fear that the tightening of races in which Trump-endorsed candidates are running will prompt them to follow the former president’s tactics and claim fraud if they lose.

Biden expressed the worry at a rally in New York on Sunday in support of the Democratic governor, Kathy Hochul, who is facing an unexpectedly tough battle with the Republican Lee Zeldin.

“These deniers are not only trying to deny your right to vote, they’re trying to deny your right to have your vote counted,” the president said. “I’m not joking. For these election deniers there are only two outcomes for any election: either they win, or they were cheated.”

Lake, who according to FiveThirtyEight holds a 2.5-point advantage over the Democrat, Katie Hobbs, in her race to become Arizona governor, is among the most vocal election deniers.

Branded “a really dangerous candidate” by Alejandra Gomez, co-director of the progressive advocacy group Lucha, the former TV newsreader turned Maga extremist has refused to say she will accept the result if she loses.

“I will accept the results of this election if we have a fair, honest and transparent election,” Lake told ABC last month.

Vance, in Ohio, chipped away steadily at the Democrat Tim Ryan’s lead through the summer and holds an advantage of almost five points, FiveThirtyEight said.

The author of the bestselling memoir Hillbilly Elegy once asserted the 2020 election was stolen from Trump but has walked back that stance and focused instead on crime and the economy in a race that could prove pivotal for Senate control.

The importance of victory in Ohio to Republicans, and for Trump’s rightwing messaging for a 2024 run, was reflected in the former president’s decision to rally for Vance on Monday night in his final public appearance before the midterms.

Ryan has distanced himself from the economic policies of the Biden administration, in an attempt to attract working-class support. Yet Trump remains popular in Ohio, his 55% approval rating about 20 points higher than Biden’s.

Two other key Senate races show momentum for Trump acolytes. The troubled Walker in Georgia is now eclipsing Democratic incumbent Raphael Warnock by almost 1.5 points after trailing since June and Oz, who has mocked his Democratic opponent, John Fetterman, over his health, is nudging ahead in Pennsylvania.

In Arizona, the Democratic senator Mark Kelly has seen Masters close to within two points after a rightwing political action committee spent $5m (£4.4m) to support him.

“It’s because of Trump’s strength, and the fact he’s so defiant so often, that somehow he appeals to a segment of voters that many of us don’t know,” Gergen said. “It’s almost as if we’ll wake up Wednesday morning and wonder what country we’re looking at.”