That was close to what the Obama campaign wants, and considerably different from Romney's earlier insistence that the race is a referendum on the president's performance in office.
Already, there are examples of concern from Republican candidates in other races, some subtle, others less so.
In Arizona, Rep. Jeff Flake recently began airing a commercial that accuses Democrat Richard Carmona of being Obama's "rubber stamp," a candidate whom the president recruited to run for the Senate to "help push his agenda." The ad doesn't say so, but Obama would need support in the next Congress only if he defeats Romney this November and wins four more years in the White House.
In North Dakota, Rep. Rick Berg, also running for the Senate, promises in an ad he will "serve as a check on Obama's failed policies" by fighting to repeal Obamacare, reduce government regulation and scale back the debt.
Both men are favored to win their races, taking place in states that Romney is expected to carry.
Nervousness first surfaced publicly among Republican Senate candidates two weeks ago, with the disclosure of a video of Romney saying 47 percent of Americans pay no income taxes and a like percentage view themselves as victims who are entitled to government benefits. As a candidate, he said, "my job is not to worry" about them.
Linda McMahon, making a second try for a Senate seat from Connecticut, quickly expressed a different opinion. "I disagree with Governor Romney's insinuation that 47 percent of Americans believe they are victims who must depend on the government for their care," she said in a statement released by her campaign.
Appointed Sen. Dean Heller, in a competitive race in Nevada, said, "My mom was a school cafeteria cook, so I have a very different view of the world than the one Romney expressed."
Former Wisconsin Gov. Tommy Thompson, running for the Senate, said, "The presidential thing is bound to have an impact on every election." His remark produced a rebuttal from former New Hampshire Gov. John Sununu, a top Romney surrogate, who said: "My good friend Tommy Thompson sounds like Barack Obama, blaming it on somebody else."
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.