CLEVELAND—In the state that may again determine the presidency, voters started casting ballots Tuesday as Barack Obama struggles to thwart a John McCain victory in Ohio four years after it tipped the election to President Bush.

Both candidates visit often while spending millions of dollars flooding TV and radio with advertisements, mailboxes with literature and even voicemail with automated phone calls to get supporters to the polls, particularly during the one-week window in which people can register and vote in one swoop.

Early participation appeared light; officials in the state’s largest counties that are home to Cleveland, Cincinnati, Toledo and Dayton each reported several hundred ballots cast by afternoon. Many of those who voted cited convenience.

“I wanted to avoid the traffic and the people,” said Charlene Glass, 49, of Cleveland Heights. A first-time voter, she backed Obama and expressed her enthusiasm for a black candidate. In Dayton, Terri Bell, 49, chose McCain because of his experience and his military service. “I have a lot on my plate. I wanted to do this early,” she said.

At stake: 20 electoral votes — perhaps, the presidency itself.

Most recent state polls show a dead heat; others give McCain an edge. National surveys show Obama slightly ahead if not more. The disparity underscores the difficulty Obama is having in closing the deal in this pivotal state. He’s a first-term senator from Chicago with a liberal voting record and would be the country’s first black president.

In all, 270 electoral votes are needed for victory.

Ohio is crucial to McCain’s electoral strategy. Bush narrowly won the state, and a loss for McCain here would be very difficult to make up with victories elsewhere given that the political landscape favors Democrats and several other key states are tilting toward Obama.

Obama, however, now leads McCain in enough other states Bush won in 2004 that he could lose Ohio and still reach the 18 electoral votes he would need if he carries all the states Democrat John Kerry did in 2004. Still, winning Ohio itself could do the trick. Every factor is at play in Ohio. Thus, every question will be tested.

Among them: Can Republican McCain overcome his links to the deeply unpopular Bush and a weakened state party and prevail in a state that suffered large losses of manufacturing jobs and large numbers of Iraq war deaths? Can Democrat Obama overcome voter concerns about his voting record and race among the many blue-collar workers in this culturally conservative, deeply divided state? Obama got shellacked here by Hillary Rodham Clinton in the Democratic primary: She carried 83 of 88 counties as white, working-class voters flocked to her economic populist message. Therefore, Obama is copying Gov. Ted Strickland and Sen. Sherrod Brown, Democrats who went into Republican areas and boosted turnout to narrow GOP margins.

“Democrats too often have forgotten about places like this,” said former Mississippi Gov. Ray Mabus, an Obama supporter who recently met with some two dozen rural voters in London in western Ohio. “They have forgotten about small-town America, rural America, agricultural America and taken it for granted that we’re going to vote the other way.”

On Monday, the state Supreme Court and two federal judges upheld the ruling by Democratic Secretary of State Jennifer Brunner that allows new voters to register and cast an absentee ballot on the same day from Tuesday through Oct. 6. Republicans argued that Ohio law requires voters to be registered for 30 days before they cast an absentee ballot.

The Ohio GOP asked the 6th U.S. Circuit Court of Appeals in Cincinnati on Tuesday either to stop same-day voting or require elections official to separate those ballots so the registrations can be verified. But Brunner already has instructed election officials to segregate those ballots and verify the registrations before counting them. A three-judge panel of the federal appeals court denied the request later in the day.