President Barack Obama will travel to Massachusetts on Sunday afternoon to campaign for Democratic Senate candidate Martha Coakley — a risky bet that puts Obama’s own credibility on the line on behalf of a weak candidate in hopes of averting a loss that would shatter the party’s 60-seat Senate supermajority.

Obama’s trip represents a stark, late recognition not just that Coakley may lose, but also that her defeat can’t be spun away. The defection of independent voters and some Democrats in one of the nation’s most liberal states would deal a stunning, and possibly fatal, blow to the centerpiece of Obama’s first-year agenda, health care reform, which congressional leaders would be left trying to jam through using procedural loopholes.

“It’s all about 60,” said a senior White House official.

Obama acknowledged the stakes in a robocall that Massachusetts voters began receiving Friday.

“I rarely make these calls, and I truly apologize for intruding on your day, but I had to talk to you about the election in Massachusetts on Tuesday, because the stakes are so high," he opened, going on to acknowledge that the outcome of the health care debate would depend on the state’s vote.

Obama’s decision came at the last minute, and after press Secretary Robert Gibbs had denied repeatedly this week that Obama had any plans to visit the state. The scramble that accompanied today’s announcement bore his comments out — Coakley and her allies won’t have time to shift their campaign’s television advertising to echo and amplify the president’s visit.

The logic of Obama’s visit is mathematical: Coakley’s polling, a Democrat involved in the race said, has shown that certain key Democratic demographics, including less affluent women and African-Americans, don’t support her in the overwhelming numbers Democrats had expected.

“A huge block of voters who have a favorable opinion of Obama aren’t with Coakley,” the Democrat said. “He’s got to go get them for her, or she loses.”

Coakley’s polling reflects other polls that show Brown closing the gap fast. A Suffolk University poll released Thursday night gave Brown a 4-point lead, carried by strong support from independent voters.

The polling suggests that Obama cannot simply win a referendum on his agenda: The poll found that only 36 percent of voters support pending health care legislation.

Obama will have to cut through a noisy Babel of competing messages coming at voters, even from the Coakley campaign.