AMES, Iowa — President Barack Obama is poised to eke out a victory in the race for the 270 electoral votes needed to win re-election, having beaten back Republican Mitt Romney’s attempts to convert momentum from the debates into support in all-important Ohio, according to an Associated Press analysis a week before Election Day.

While the Democratic incumbent has the upper hand in the electoral vote hunt, Romney has pulled even, or is slightly ahead, in polling in a few pivotal states, including Florida and Virginia. The Republican challenger also appears to have the advantage in North Carolina, the most conservative of the hotly contested nine states that will determine the winner.

While in a tight race with Obama for the popular vote, Romney continues to have fewer state-by-state paths than Obama to reach 270. Without Ohio’s 18 electoral votes, Romney would need last-minute victories in nearly all the remaining up-for-grabs states and manage to pick off key states now leaning Obama’s way, such as Iowa or Wisconsin.

To be sure, anything can happen in the coming days to influence the Nov. 6 election.

The AP analysis isn’t intended to predict the outcome. Rather, it’s meant to provide a snapshot of a race that has been stubbornly close in the small number of competitive states all year. The analysis is based on public polls and internal campaign surveys as well as spending on television advertising, candidate visits, get-out-the-vote organizations and interviews with dozens of Republican and Democratic strategists in Washington and in the most contested states.

The analysis shows that Obama probably would win with at least 271 electoral votes from 21 states, including Ohio, Wisconsin and Iowa, and the District of Columbia. Romney seems on track for 206 from 23 states, including North Carolina. Obama won that state in 2008 and campaigned aggressively there this year. But Obama’s team acknowledges it is the most difficult state for him to win, and he’s paid less attention to it recently.

Colorado, Florida, Nevada, New Hampshire and Virginia, with a combined 61 votes at stake, could go either way.

“I’m counting on Iowa! Iowa may be the place that decides who the next president is!” Romney said on one of two visits to the state last week. In Ohio last week, a hoarse Obama reminded a Cleveland audience near the end of a six-state marathon: “I need you, Ohio. America needs you, Ohio.”

Romney is banking on what his supporters say is late momentum. Obama is betting that his aggressive effort to register and lock in early voters, mainly Democratic-leaning younger and minority voters, will give him an insurmountable advantage heading into Election Day, when more Republicans typically vote than Democrats.

About 35 percent of voters are expected to cast their ballots before Nov. 6, either in person or by mail. More than 5 million people already have voted. No votes will be counted until Nov 6, but some states report the party affiliation of people who have voted. Democrats have the edge in Iowa, Nevada and North Carolina, according to state figures and data collected by the United States Elections Project at George Mason University. Republicans have the early edge in Colorado.

Obama, who won in 2008 in places where Democrats had not for a generation, continues to have several routes to electoral victory. His easiest: win Ohio, Iowa and Wisconsin, which are leaning his way. He could keep the White House with victories in Ohio, Wisconsin and Nevada. If he loses Ohio, he could prevail by sweeping New Hampshire, Iowa, Wisconsin, Nevada and Colorado.