NEW YORK – The political conventions are finished, the Olympics are history and summer vacation is over. It’s time to pick a president.

The country enters the fall campaign divided between Republican President George Bush and the Democratic challenger, Sen. John Kerry. Americans signaled slightly more support for Bush in recent polls, but they still refuse to rally strongly behind either man.

The fate of the presidency and the course of the nation could come down to how the two men handle the next nine weeks on the battleground of perhaps 20 closely divided states, in the coming barrage of television ads and in their face-to-face debates.

Bush enters the fall stretch run with some momentum, energizing his base of supporters and apparently making headway with “swing” voters.

Even before he started speaking Thursday night at the Republican National Convention, Bush had reached 90 percent support from Republicans for the first time this year and moved ahead of Kerry in at least one poll. Pollster John Zogby found Bush leading by 46 percent to 44 percent after trailing the week before by 43 percent to 48 percent.

While the survey had a margin of error of plus or minus 3.2 percentage points, meaning the two men were statistically tied, it did suggest gains by Bush.

That was no accident.

Much of the Republican convention was aimed at firing up the party’s conservative base, from a platform that adds anti-gay marriage language to an incendiary keynote speech from Sen. Zell Miller, D-Ga., that accused Kerry of being a wimp on defense.

Bush political adviser Karl Rove wants to mobilize the estimated 4 million Christian conservatives who sat out the 2000 election.

Rural conservatives are another Rove target. Bush advisers say too many still vote Democratic in states such as Minnesota, Wisconsin and Pennsylvania, and too many stay home. Bush’s advisers want to boost turnout among rural conservatives by nearly 10 percent.

“It’s all base,” said a veteran congressional Republican strategist who spoke on condition of anonymity. “The conservative base is bigger than the liberal base. There’s more to work with.”

Zogby said Bush “widened his lead in red (Republican) states and tightened things up considerably in blue (Democratic) states.”

But he cautioned that a majority of Americans still think the country is headed in the wrong direction and warned that Bush’s post-convention bounce was likely to dissipate.

“The battle is now engaged,” Zogby said.

Both sides also will try to influence swing voters, those not firmly committed to Bush or Kerry and who tend to swing back and forth. The campaigns’ first choice is to win their votes. Failing that, they’ll strive to sour swing voters on the opposing candidate in hopes that they’ll decide not to vote at all.

A focus group of 21 undecided voters in Cincinnati, Ohio, also suggested gains by Bush. After watching the convention but before Bush’s speech, two had made up their minds to vote for him. After Bush’s speech, 13 made up their minds to vote for Bush, and one made up his mind to vote for Kerry.

Once solidly Republican turf, the Cincinnati area has been a problem for Bush; it’s one reason he’s struggling to hold the state he won narrowly in 2000. Of the focus group members, 12 had voted for Bush last time, only to slip into the undecided column. Yet by Thursday night, 15 of the 21 said they would vote for him this year.

“This was a home run,” said Frank Luntz, who moderated the group for MSNBC. He called it the second most effective convention speech he’d seen at reaching swing voters, after Democrat Al Gore’s speech in 2000.

Yet Luntz, too, cautioned that Bush remains vulnerable, particularly on jobs and the economy. The one weak focus-group reaction to his speech was when he said the country had turned the corner on jobs. “They didn’t believe,” Luntz said. But he concluded that, “considering the economy and the war in Iraq, Bush couldn’t be in a stronger position.”

Even with a slight lead, Bush will have to fight all the way to Election Day to keep his job. And Kerry showed Thursday night that he plans to fight him every step of the way; at a midnight rally in Springfield, Ohio, he slammed Vice President Dick Cheney for daring to attack him as weak on national security after Cheney avoided military service in Vietnam and condemned Bush for “misleading” Americans into war in Iraq.

Part of that fight will focus on the past, particularly over what each man did during the Vietnam War. With accusations of draft dodging, lying and betrayal of American troops, the sparring is likely to rub raw the still-painful political scars of that era.

The rest will hinge on voter perceptions of who can better protect the country from terrorist attacks, handle Iraq and improve the economy.

Bush and Kerry are certain to debate – the major-party candidates have faced off in every campaign since 1976. Drawing the biggest audience of the campaign – nearly 47 million tuned in four years ago – this year’s debates will be potentially decisive.

The bipartisan Commission on Presidential Debates has proposed three presidential face-offs: on Sept. 30 in Miami, Oct. 8 in St. Louis and Oct. 13 in Tempe, Ariz. The panel has recommended a vice presidential debate for Oct. 5 in Cleveland.

The two campaigns are negotiating the details, presumably including whether to include independent candidate Ralph Nader. Bush’s lead negotiator is former Secretary of State James Baker; Kerry’s is lawyer Vernon Jordan.

They also will make their cases in television ads and on the campaign trail.

Taxpayers will pay for the ads. Each candidate gets $75 million for the fall campaign, plus $15 million for each national party.

Kerry has already announced that he will spend at least $50 million on television ads, many targeted to certain states or regions.

Six new commercials unveiled Friday accuse Bush of breaking promises made in six cities. In Scranton, Pa., for example, the ad says that Bush went there in the 2000 campaign to promise expanded health care but failed to deliver.

Except for the debates, the campaign will be witnessed from afar by most of the country. Each party has a solid majority lock on certain states, and voters in those states will see few campaign commercials and receive no visits from the candidates.

There are only about 20 states that are so closely divided that either candidate could win, and those are where both men will spend most of their time and money.

Those states are Arkansas, Colorado, Florida, Iowa, Louisiana, Maine, Michigan, Minnesota, Missouri, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Oregon, Pennsylvania, Tennessee, Washington, West Virginia, and Wisconsin.