That remains to be seen, as Obama puts his prestige on the line again when he goes to the Bay State on Sunday to stump for Democratic nominee Martha Coakley, who is in a dead heat with Republican candidate Scott Brown for Ted Kennedy’s Senate seat.

“It’s white-knuckle time,” Democratic operative Phil Johnston told the Boston Herald. “This is an election we have to win. It’s key to everything the Obama administration wants to do. The stakes are high.”

In fact, the stakes are even higher for the president than they were in last year’s gubernatorial races, as he seeks to avoid losing a critical 60th vote in the Senate for his signature health care overhaul that is nearing the finish line in Congress.

If Brown wins Tuesday, Republicans pick up their 41st vote, which would be enough to sustain a filibuster and possibly kill the reform bill.

The most recent poll has Brown leading by 4 percentage points, and the Republican state senator reportedly is raising money at a rate of $1 million a day. Meanwhile, Coakley’s campaign is under fire for the way she’s run her campaign, going from front-runner to barely competitive after taking it easy following her primary victory in December.

The president’s decision to hit the campaign trail again is a stunning reversal from what the White House had been saying in recent days and reflects the concerns Democrats have over their chances Tuesday.

John Feehery, a Republican consultant, told the Herald that the trip reeks of desperation for both Coakley and Obama.

“It’s a complete meltdown, and it doesn’t seem to me that it will have much of an impact,” Feehery said, adding that Democrats he’s talked to are blaming Coakley. “You can always tell when Democrats are going to lose because they start blaming the candidate.”

But White House spokesman Robert Gibbs said Friday that Obama believes his visit will be “productive.”

“I think it’s a referendum on whose side are you on,” Gibbs said, dismissing suggestions the race is a referendum on the president himself. “I think the president sees a pretty clear distinction between a candidate in Martha Coakley who’s going to fight for Massachusetts and a candidate on the other side who feels comfortable fighting for the insurance industry and big banks.”

A spokeswoman for Brown, in response to Obama’s planned visit, called Coakley a “rubber stamp for the political machine.”

Before deciding to visit the state this weekend, the president did come to Coakley’s aid by cutting an online video for her, calling on supporters to put on their “walking shoes” and bring out people to vote.

“In Washington, I’m fighting to curb the abuses of a health insurance industry that routinely denies care,” Obama said. “I’m fighting for financial reforms to stop Wall Street from playing havoc with our economy. I’m fighting to create a new, clean energy economy.

“And it’s clear now that the outcome of these and other fights will probably rest on one vote in the United States Senate.”