Continued from page 1

This year, Mr. Obama has campaigned extensively in Ohio, and regularly asks supporters to boost some fellow Democrats. Sen. Sherrod Brown and Rep. Marcy Kaptur — both firmly in their party’s liberal wing — have received the most mentions from Mr. Obama at recent events.

The Ohio Democratic Party didn’t respond to requests for comment.

Republican presidential nominee Mitt Romney is trying to extend his own coattails, regularly asking for support for his party’s congressional candidates.

“All those down-ticket folks are mentioned, and thanked, just as they were in 2008,” said Matt Henderson, a spokesman for the Ohio Republican Party. “In terms of ‘Does it help them?’ The people are coming to these rallies to hear Mitt Romney. Of course it’s going to help, but so does having an ‘R’ next to your name on the ballot.”

Weakened in New England

That’s not the case in the liberal states of the Northeast, even though Mr. Romney’s highest political office was as governor of Massachusetts.

Though Sen. Scott P. Brown, Massachusetts Republican, endorsed Mr. Romney, he barely mentions his state’s ex-governor on the campaign trail, opting instead to tout his own record as “the second most bipartisan member of the Senate.”

Republican Linda McMahon, running again for a Senate seat in Connecticut, recently cut an ad featuring people who are voting for her — as well as Mr. Obama.

“The terrain the candidate operates on defines the kind of campaign they run,” said Kyle Kondik, a political analyst at the University of Virginia’s Center for Politics.

Some candidates, though, will have a tougher time distancing themselves from the top of their ticket.

In Virginia, former Gov. Tim Kaine served as the president’s hand-picked chairman of the Democratic National Committee from 2009 to 2011 and spoke with Mr. Obama before deciding to run for the seat of retiring Sen. Jim Webb.

Mr. Kaine has tried to stake out some differences between himself and Mr. Obama, but there is not much distance between the two in the polls: The latest Real Clear Politics average has Mr. Obama tied with Mr. Romney in Virginia and Mr. Kaine ahead by 2 points against Republican George Allen.

Nevertheless, Mr. Kaine has taken umbrage with the way his opposition often tries to frame the connection.

“One day I was driving down Interstate 95, and I saw a big billboard with a picture of me and President Obama on it, and the billboard said, ‘Tim Kaine: Obama’s senator, not Virginia’s,’” Mr. Kaine said.

“Now, I liked being called senator before the election, so that was good. But the implication of the billboard was it is anti-Virginian for me, and that I’m somehow anti-Virginian, because I support the president of the United States. I am a supporter, and I am a friend of the president of the United States, and I want him to be re-elected. But whether somebody wants the president to be re-elected or not, let there be no mistake: It is not anti-Virginian to support the president of the United States,” he said.