WASHINGTON — Senator McCain is entering the final eight weeks of the presidential campaign surging in the polls following his party’s national convention, with the selection of Governor Palin as his running mate appearing to have closed a lingering gap with Senator Obama.

The race now turns to the battleground states and to the four fall debates, which will take on heightened importance in a neck-and-neck campaign.

A group of polls over the past few days indicate that Mr. McCain picked up a sizable bounce from the Republican National Convention in St. Paul, Minn., where it was Mrs. Palin who stole the show with an electrifying and highly watched speech accepting the vice presidential nomination.

Two surveys released last night by CBS News and ABC News showed Mr. McCain holding a lead within the margin of error among registered voters, while a USA Today/Gallup poll gave him a four-point lead among registered voters, 50% to 46%. A CNN survey of registered voters had the race tied at 48%. The polls a week ago showed Mr. Obama opening a modest but significant lead following his party’s convention in Denver.

While political strategists caution against reading too much into national polls, the shift in the last week suggests that less than two months before Election Day, a presidential campaign long thought to favor the Democrats is a statistical dead heat.

The pick of Mrs. Palin, a first-term Alaska governor, appears to have energized a Republican base wary of Mr. McCain, and according to the poll conducted by ABC News and the Washington Post, the Republican ticket has opened up a lead among white women, who had been supporting Mr. Obama.

“What Palin did was put the speed brake on Obama’s campaign,” a Democratic strategist who is associate dean of Boston University’s College of Communication, Tobe Berkovitz, said. He added, however, that Mr. McCain’s post-convention bounce may fade in the next two weeks. “Let the dust settle,” he said.

The party conventions also crystallized the strategies upon which each campaign is focused. Mr. Obama and his running mate, Senator Biden, are intent on tying Mr. McCain to the unpopular Bush administration, while Mr. McCain and Mrs. Palin are branding themselves as mavericks who will bring reform to Washington.

That battle played out yesterday in a pair of television ads. A 30-second spot from the McCain campaign casts the two Republicans as “the original mavericks” and highlights their efforts to fight entrenched interests in Washington and Alaska.

“He fights pork-barrel spending. She stopped the Bridge to Nowhere,” a narrator says in the ad. “He took on the drug industry. She took on Big Oil. He battled Republicans and reformed Washington. She battled Republicans and reformed Alaska. They’ll make history. They’ll change Washington.”

The Democrats responded late in the day with an ad accusing Mr. McCain and Mrs. Palin of lying about their records. “They call themselves mavericks. Whoa,” the narrator says. “The truth is they’re anything but.” The spot goes on to highlight Mr. McCain’s support for the Bush administration and cites Mrs. Palin’s previous backing for the widely reviled “Bridge to Nowhere” in Alaska, which has become a rallying call for changing the congressional earmarks process. “Politicians lying about their records? You don’t call that maverick. You call that more of the same,” the announcer concludes.

The ad followed a stepped-up attack from Mr. Obama earlier in the day, when he criticized Mrs. Palin at a campaign stop in Michigan for distorting her position on the bridge, which would have sent more than $200 million in federal money to connect a tiny island to the Alaska mainland. “I mean you can’t just make stuff up,” Mr. Obama said. “You can’t just re-create yourself. You can’t just reinvent yourself. The American people aren’t stupid.”

The strong words signaled a shift from Mr. Obama, who a day earlier had avoided direct criticism of Mrs. Palin in an appearance on ABC’s “This Week.”

Democratic strategists said yesterday that Mr. Obama had been correct to focus his attention on the top of the Republican ticket and not “take the bait” and attack Mrs. Palin’s lack of experience, particularly with Republicans acutely sensitive to the hint of sexism from Democrats. “You can’t attack a woman in that way,” a Democratic consultant, Hank Sheinkopf, said, adding that, fairly or not, Mr. Obama had to be especially careful because of the race- and gender-based tensions the campaign has exposed.

While the Democratic strategists warned the Obama campaign against overreacting to the phenomenon of Mrs. Palin, a Republican consultant, Whit Ayres, said there was a risk in ignoring her. “It’s the no. 2 that’s providing the energy for the ticket,” he said.

Strategists on both sides said the race could ultimately turn, as in past elections, on organization. The Obama campaign will look to turn out young voters in record numbers, particularly in states such as Colorado, Iowa, and Virginia that it aims to swing to blue from red. The McCain campaign, meanwhile, will need to harness the enthusiasm for Mrs. Palin into a strong turnout from the party’s base.

The election could also hinge on the debates, which could draw record viewership after the two highly watched conventions. The first presidential debate is September 26 in Mississippi, with additional matchups on October 7 in Nashville and October 15 at Hofstra University on Long Island. A much-anticipated vice presidential debate between Mrs. Palin and Mr. Biden is scheduled for October 2 in St. Louis.