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Washington (CNN) -- Maybe Mitt Romney's campaign team isn't so bad after all.
After months of criticism, much of it from fellow Republicans, the machine managing Romney's presidential bid has him gaining support in the final weeks of the race.
The latest polls show Romney catching or slightly passing President Barack Obama in both the overall race and in some of the battleground states still considered up for grabs and therefore vital to both candidates' chances.
Some of those polls also show a hike in Romney's favorability rating, indicating more respondents were supporting the former Massachusetts governor instead of simply opposing Obama.
The late surge follows a rocky period for Romney following the rugged Republican primary campaign, including an ultimately nondescript GOP convention and some unforced errors, such as his so-called 47% comments that were secretly recorded at a fundraiser.
Then, a strong performance in the first presidential debate -- coupled with a lackluster effort by Obama that night -- served as the catalyst for what the Romney campaign insists is a late surge with just over three weeks until the November 6 election.
Polling since the October 3 debate in Denver shows Romney moving up.
In the latest CNN poll of polls -- an aggregate of all the latest major polls -- Romney was slightly ahead of Obama by 48%-47% and pulled ahead of the president in the crucial state of Florida by 49%-46%. However, Obama maintained his lead in two other key battleground states -- by 50%-47% in Ohio and 48%-47% in Virginia. Most analysts agree that whoever wins two of those three states will almost certainly win the White House.
Rich Galen, a conservative commentator who worked in the past for former House Speaker Newt Gingrich, said the rise in Romney's favorability numbers was due partly to support from right-leaning voters who don't like Obama but weren't yet sold on the Republican until the first debate.
"I was really struck by that because that is probably the first robin of spring that demonstrates how people are looking differently at Romney," Galen told CNN in an interview on Monday.
At the same time, Galen acknowledged such "leaners" and "uncommitted" voters were unlikely to support Obama in any case, and that the new poll results "didn't indicate they changed their minds" from voting for the president.
"It is those people who I think saw something in Romney that they just hadn't been prepared for," Galen said, adding that voters such as Republican leaners wanted to be convinced. "It's like going to a movie that everybody else says is a great movie. You have to see it for yourself."
To Galen, one reason for the turnaround was a patient strategy by the Romney campaign that waited until the home stretch to unveil a long expected shift toward the middle by the candidate who described himself as "severely conservative" during the primaries to try to appeal to the right-wing base.
"They hold their fire, hold their fire, hold their fire, and then they sprint to the finish," Galen said, referring to what he called a "change in what he's saying and how he's saying it."
The shift "tells me that they had planned for a late-game surge," he said.
Other factors point to such a tactic. For example, Romney could have used the Republican National Convention, when he and the party were the focus of the national political debate, to move toward the middle.
Instead, he waited until the first debate, when he also had the full force of campaign funding available after being limited to primary contributions only until after he formally accepted the nomination at the Tampa convention in late August.
In the run-up to the first debate, New Jersey Gov. Chris Christie -- a key Romney surrogate who delivered the keynote address at the GOP convention -- predicted the initial showdown between Romney and Obama would amount to a restart of the race.
Voters would "start tuning in on Wednesday night, and when they do, Gov. Romney will lay out his vision for a better and greater America, for greater opportunity, for all of our citizens," Christie told NBC's "Meet the Press" three days before the debate. "And I think that's when you're going to see this race really start to tighten and then move in Governor Romney's direction."
His prescient comments undercut party efforts to minimize expectations for the first debate, but not everyone was ready to credit the Romney team for choreographing the comeback.
Ron Brownstein, the National Journal editorial director and CNN senior political analyst, said Obama's poor performance had as much to do with it as Romney's strong showing.
The Romney team "kind of reshaped his image at the debate to make him a more moderate figure," Brownstein said, adding it "would have been dangerous to do that earlier."
Romney "talked to the voters who are dissatisfied with Obama and reminded them why they were was dissatisfied and helped cross the threshold on why he would do better," while Obama "did nothing to frame the case against Romney" or explain what he would do in a second term to make things better, Brownstein said.
Until the first debate, he explained, Obama benefited from "a slice of the electorate who were clearly dissatisfied with his first term, were not sure he deserved a second term, but weren't sure if Romney was a viable alternative," thereby providing the president some margin of comfort.
"I think that permanently changed at the first debate," Brownstein said. "It doesn't mean Romney's going to win, but we are in a structurally different race."
Obama's approval rating, hovering at 50%, is "just enough to get elected" and the president still leads in Ohio, Brownstein noted, but "the idea of any kind of cushion is what is gone."
New ABC News/Washington Post and Politico/George Washington University national polls showed the rise in Romney's favorability ratings, with the Politico-George Washington survey putting him even with the president on that question.
Romney and his campaign have sought to frame the election as a referendum on Obama's presidency, citing high unemployment, slow economic growth from the recession and chronic federal deficits and debt as reasons to deny a second term.
For their part, Obama and Democrats have tried to make the election about competing visions for the future, arguing Republican proposals to repeal major legislation such as health care and Wall Street reforms while expanding tax cuts without identifying additional revenue sources would stall a sluggish but steady recovery.
To Brownstein, Obama needs to spell out how his plans for a second term would be better for the country than what Romney proposes.
"Among the many challenges facing Obama in the next debate, the first among equals is convincing wavering voters that he has a plan to make the next four years better than the last four --something he almost utterly failed to convey at the first debate," Brownstein said.
Galen said those who were quick to criticize the Romney campaign during tough stretches in the primaries and recent months may need to reassess.
"If things turn around and start looking good," he said, "I think you have to give them credit."
CNN Political Editor Paul Steinhauser contributed to this report