Mrs. Clinton's campaign has concluded that at least two traditionally Republican states, Georgia and Arizona, are realistic targets for her campaign to win over. And Republican polling has found that Mr. Trump is at dire risk of losing Georgia, according to people briefed on the polls, who spoke on the condition of anonymity.
Mrs. Clinton now holds such a strong upper hand that Priorities USA, a "super PAC" backing her campaign, may direct some of its war chest into Senate races, two people said, and may begin broadcasting ads for those contests as soon as next week. Congressional Democrats also hope to persuade Mrs. Clinton to continue pouring money and campaign resources into states like Virginia and Colorado, where they believe her victory is assured, in order to lift other Democratic candidates.
In a signal of Democrats' growing focus on the House and Senate, Mrs. Clinton used a visit on Tuesday to Miami to attack both Mr. Trump and Senator Marco Rubio, whom Mrs. Clinton blasted for what she described as his indifference to climate change.
"We need to elect people up and down the ballot, at every level of government, who take it seriously," Mrs. Clinton said, adding, "It is an unacceptable response for Marco Rubio, when asked about climate change, to say, 'I'm not a scientist.'"
Mrs. Clinton's campaign chairman, John D. Podesta, told reporters that she would continue to call out down-ballot Republicans. Mr. Rubio is among the Republicans whom Priorities USA may seek to defeat, if the group decides to intervene in Senate races, one strategist said.
The nightmare possibility for the party is that swing voters punish the party because of Mr. Trump, the anti-Trump Republicans stay at home and Mr. Trump's base casts a ballot for him and then leaves the polls. Under those conditions, Senate races in places like Pennsylvania and North Carolina could fall to Democrats, while Senate and House races in places like Missouri, Arizona and Kansas could move to the center of the battlefield.
Already, Republicans view Mr. Trump's sharp downturn in the presidential race as having jeopardized their majorities in Congress. A poll published on Tuesday by NBC News and The Wall Street Journal found Mr. Trump trailing Mrs. Clinton by nine percentage points nationally and drawing just 37 percent of the vote. No major-party nominee since World War II has received a smaller share of the vote. But in an illustration of the bind Republicans are in, the poll found that three-fourths of Republicans believed their candidates should stay loyal to Mr. Trump.
In Nevada, the Republican candidate for Senate, Representative Joe Heck, withdrew his support from Mr. Trump over the weekend, and is facing a furious backlash.
Sandie Kirwin, a Las Vegas retail manager supportive of Mr. Trump, said she might now vote for a Democrat over Mr. Heck in a critical Senate race.
"I think of Joe Heck the same I do of any Republican not supporting Donald Trump," said Ms. Kirwin, 52. "I will never support any of them, and I will do what I can to get them out of office."
In Pennsylvania, Jaye Steuterman, a registered Republican and a real estate agent in Doylestown, said she was still undecided on which presidential candidate to vote for. She said she was deeply unsettled by Mr. Trump's past comments about forcing himself on women, but that might not be enough to stop her voting for him.
"I don't know what's more important to me — that, or the fact that Hillary is a liar," Ms. Steuterman said.
In the Senate race, she is inclined to vote for Mr. Toomey because he is a Republican, but her decision could depend on whether he supports Mr. Trump.
Three Democratic congressional candidates have started ruvnning ads this week that showcase footage of Mr. Trump describing sexual assault in graphic terms, from a 2005 recording. Gov. Maggie Hassan of New Hampshire, who is challenging Senator Kelly Ayotte, used the footage in a campaign video on Tuesday, saying Ms. Ayotte recently denounced Mr. Trump only to "protect herself."
The NewYork Times Reports