Donald Trump at the first presidential debate in New York on September 26. Win McNamee/Getty Images Donald Trump's slip in the polls this past week reportedly has Republicans worried their choice at the top of the ticket could drag down congressional races they need to win to maintain control of the House and the Senate.

While some notable Republicans have denounced or distanced themselves from Trump, many running for reelection have stuck by their party's choice for the Oval Office.

But in an article published Wednesday, several anonymous sources told The New York Times that could soon change — especially if the Manhattan billionaire performs poorly at the second presidential debate, set for Sunday in St. Louis.

Pundits, focus groups, and then polls concluded that Trump's Democratic opponent, Hillary Clinton, won the first debate September 26, which was followed by a week of disagreement between Trump and former Miss Universe Alicia Machado, whom he called fat while encouraging people to dig into her past.

While Republican control over the 435-member House of Representatives isn't likely to change, Democrats could reclaim the Senate this election. Of the 34 seats that are up for grabs, Republicans hold 24 and Democrats hold 10.

But most of those GOP seats are filled by tea-party members who swept into office in 2010 after the Democratic-controlled Congress passed the Affordable Care Act, according to Ballotpedia. If Clinton wins the presidency and her running mate, Tim Kaine, becomes the tiebreaking vote in the Senate, Democrats would need to win just 16 of the open seats to have a majority.

Democrats are projected to take back several of those seats, and the likelihood has grown even more favorable in the past week. Nate Silver's election forecast at FiveThirtyEight now has Democrats with a 61.5% chance of winning back the Senate.

The next presidential debates could make it even clearer whether congressional Republicans seeking reelection will have to run from their nominee to save themselves. The second debate between Trump and Clinton will begin Sunday at 9 p.m. ET at Washington University in St. Louis.