Correction: An earlier version of this story misstated the number of Cuyahoga County voters who had cast ballots in person the Friday before the 2008 election. This version has been corrected.

Democrats fought all the way to the U.S. Supreme Court and won to keep Ohio polls open to all voters this weekend, and they were making the most of it in this Democratic stronghold Saturday.

As a line of shivering voters wound down the stairs of the Cuyahoga County Board of Elections and around the downtown block, a steady stream of vans with Obama signs pulled up to the curb and disgorged more voters to join the line.

Across the street, campaign volunteers grilled hamburgers and hot dogs, and passed out hot chocolate and coffee.

And then there was Stevie Wonder, who showed up for an unannounced concert for about 100 spectators a few blocks away at Cleveland State University, before stopping by the polling place in a black SUV to the gasps of waiting voters.

Public polls in Ohio show President Obama holds a wide lead over Mitt Romney among voters who have voted since polls opened to early voters Oct. 2.

Explore the 2012 electoral map and view historical results and demographics

Four years ago, early voting was a option for each of the five weekends during the voting period. This year that was reduced to one. Some Ohio election boards, particularly in urban counties, have been reporting that fewer people have so far taken advantage of the in-person early-vote option this year, when polls until now have been open only on workdays.

But the Ohio secretary of state’s office said Saturday that, statewide, 1.6 million people had voted by mail or in person as of Friday, a figure that puts the state on track to top 2008 early-vote tallies.

In Cuyahoga, 36,578 had voted as of Friday; in 2008, that number was 43,402 . In 2008, there were nine additional early voting days here, and 9,933 people voted on those days.

More than 3,000 people voted Saturday.

Republican state leaders had sought to allow only military voters to cast ballots this weekend as well, but Democrats won a court battle arguing that if polls were open to some, they must be open to all.

That means Obama’s effort here hinges on getting a huge turnout this weekend, particularly Sunday when buses will roll straight from church services to the polls.

“The more people who vote in Ohio, the better President Obama’s chances of winning there are,” the campaign’s national field director, Jeremy Bird, wrote in a memo to reporters Friday. A study released last month by the Lawyers’ Committee for Civil Rights Under Law underscored why early voting favored Democrats.

The study found that black voters — who overwhelmingly favor Obama — used early in-person voting at approximately 26 times the rate of white voters.

“This is what works for working-class folks. If they have a 9-to-5 job, they’ve got kids to pick up and a lot going on, the weekend is when they’ll be able to get time to go vote,” said Michael Gillis, a spokesman for the Ohio AFL-CIO, which is running its own mass get-out-the-vote effort this weekend.

They are voters like Brenda Herbert, 61, who came to vote in Cleveland on Saturday with her 93-year-old father, Clarence Yarbrough. She said she must take care of her grandchildren Tuesday while her daughter goes to a new job.

“I said, ‘We have got to come down and vote today.’ Because I don’t want to wait until Tuesday at 6 o’clock or later to come vote. What if I don’t make it? What if something happens with the children?” said Herbert, who lives in Shaker Heights.

She was carrying a flier distributed in Cleveland neighborhoods — she picked hers up at a local restaurant — advertising a steady stream of celebrities who were to discreetly visit the early-voting center this weekend, including Will.I.Am, Vivica A. Fox and John Legend.

Republicans have insisted that public polling has not captured the enthusiasm of their own early voters and that they will take advantage of the final vote weekend as well.

“We have been saying for months that we are prepared to match the Obama campaign volunteer for volunteer, door-knock for door-knock and phone call for phone call through Election Day. That remains the case in the final 72 hours,” said Romney Ohio spokesman Chris Maloney.

By Saturday, voting in Republican-leaning Allen County in northwest Ohio had already surpassed its early-vote totals from 2008. Just shy of 13,000 voters had cast early ballots in person or by mail, and local officials expected the numbers would easily pass 14,000 by the end of Monday.

Bob and Connie Warniment drove 15 minutes from nearby Delphos to cast ballots for the Republican nominee Saturday after their daughter encouraged them to vote early so they could get to their cabin in Michigan a few days before they had planned.

“The working people might go for that option because the lines are long and they might have to get up earlier to vote,” Connie Warniment said.

But here, too, there were signs of an aggressive Democratic get-out-the-vote effort, including Obama voters who had already cast their ballots but had returned at the campaign’s urging with friends or family Saturday.

In 2008, Obama won Ohio in part by driving up Democratic turnout in counties that were still won by Sen. John McCain. In Allen, for instance, Obama got 3,000 more votes than Sen. John F. Kerry did four years earlier, in a county where 50,000 people voted.

The tangling over how and when to count ballots in Ohio isn’t over. Late Friday, Republican Secretary of State John Husted issued a new directive outlining information that must be included on the outside of a provisional ballot — directing election boards not to count a ballot if a section of the form that’s supposed to be filled out by poll workers is empty.

Lawyers with the Northeast Ohio Coalition for the Homeless have already challenged the new directive in federal court, in an issue that could become relevant if the Ohio contest is tight.

O’Keefe reported from Lima, Ohio.