That approach would be unusual enough for a Democrat in a year in which many feel the need to distance themselves from the administration, but it is virtually unfathomable for a Republican. That both candidates are trying to leverage their ties to Mr. Obama underscores how popular the president is here and how unpopular his rival, Mitt Romney, is, even though he once served as the state’s governor. Mr. Obama is expected to carry Massachusetts overwhelmingly in November.

Image An ad for Senator Scott P. Brown of Massachusetts shows the president telling him, “Good job.” Credit... Associated Press

Mr. Brown’s new ad is a clear overture to independent voters, who make up more than 52 percent of the state’s electorate. It seeks to reassure them that splitting their ticket — voting for a Democrat for president and a Republican for the Senate — can still mean that things will get done in Washington.

The commercial follows weeks of other ads in which various former Democratic officeholders have endorsed Mr. Brown; on Friday, his campaign rolled out a “Democrats for Brown” coalition that includes a state representative, Christopher G. Fallon of Malden, and other officials.

The strategy may be paying off. Over the last few weeks, Mr. Brown appears to have been inching ahead of Ms. Warren in the polls, though the race still seems to be within the statistical margin of error. Significantly, he has been building a strong lead over Ms. Warren among independents. Polls suggested that he was attracting as many as one in five Democrats and one in four Obama voters.

“The race is going to be won or lost among the independents,” said David Paleologos, a pollster at Suffolk University in Boston. “The onus is on the Warren campaign to define and clarify what having a Republican Senate means and to force people to vote straight Democratic.”