What a difference a debate makes.

Republican Mitt Romney has opened a large, 7 percentage-point lead over President Barack Obama in must-win Florida, according to a new poll of likely voters conducted for The Miami Herald/El Nuevo Herald and the Tampa Bay Times.

Romney’s 51-44 percent advantage is just on the cusp of the poll’s error margin — and it marks a dramatic 8-point shift since last month.

“Obama’s now swimming upstream,” said Brad Coker, pollster with Mason Dixon Polling & Research, which conducted the survey of 800 likely Florida voters this month and last for The Herald and its news partners, including Bay News 9 and Central Florida News 13.

The previous poll, which showed Obama with an inside-the-error-margin lead, was before last Wednesday’s debate when Obama gave a lackluster performance while Romney appeared to excel.

This latest poll showed that 5 percent of those who said they were undecided before the debate say they’ll vote for Romney. And 4 percent of those who said they favored Obama pre-debate moved away from the president — 2 percent toward Romney and 2 percent undecided.

“Obama didn’t flip one voter,” Coker said. “He didn’t gain 1 percent from the debate.”

Even Democrats were upset with Obama’s performance.

“I was disappointed,” said Phyllis Apple, a 90-year-old Democrat from Aventura. “He didn’t look like he was ready to fight. Maybe the president thought it wouldn’t look presidential.”

A top political advisor to the president, David Plouffe, acknowledged that the debate was a “wake-up call” and that the race has tightened. But, he said, he believes in the campaign’s message and its vast volunteer army that can turn out nontraditional voters who don’t necessarily get picked up in polls such as this one.

“That’s where there are real gains for us. We’ve got to find them,” Plouffe said. As for Romney’s surge, Plouffe said, “Romney picked up his easy gains ... We think the Romney gains have stopped.”

Romney’s strong performance also led people to trust him more on Medicare, the economy and foreign policy, which once was a strong suit of the president after the killing of Osama bin Laden.

But the fallout from the Sept. 11 terrorist attacks in Libya — not just the debate — might have hurt Obama as well. Also potentially helping Romney is that the economy in Florida is stuck in the doldrums, with the unemployment rate ticking up slightly last month while it fell nationally.

Romney’s biggest gain: independent voters, the swing electorate in swing-state Florida, without which Romney has no shot of winning the presidency this year.

Independents moved 24 points away from Obama and toward Romney, who’s now favored by 13 points, or 52-39, over the president.

Another huge gain came with women, who once favored Obama by double digits, and are now virtually split between the top two contenders. They moved a total of 13 points in Romney’s favor in a month.

In a sign of his need to reach out to women, Obama’s campaign has stepped up its criticisms of Romney for his opposition to abortion. The Democrats have sent out stacks of mailers to registered Florida female voters reminding them of Romney’s stances and have suggested that the Republican would want to ban some forms of birth control.