CLEVELAND – Election officials estimate that at least half of the registered voters in crucial Cuyahoga County had cast ballots by 2:30 p.m., and Democratic Party officials were hoping to push that number significantly higher to get President Obama the edge he needs in Ohio.

Despite widespread fears of polling problems in one of Obama’s key strongholds, voting has gone on with few snags throughout the day, according to elections officials. There were a handful of problems with paper ballots not entering electronic voting machines correctly, but those have been corrected without any lost votes.

“We’ve continued to have a smooth election day,” said Jane M. Platten, director of the Cuyahoga County Board of Elections.

Early voting allowed 27 percent of Cuyahoga’s voters to cast ballots by the end of Monday. On Tuesday, officials called a sampling of precincts and reported that an estimated 23 percent of the county’s voters had so far cast ballots on election day itself, with potentially busy late afternoon and evening hours still to come.

Now attention is focusing on turnout. Obama has a dramatic edge here in the county, which includes Cleveland and its closest suburbs. To win, Obama needs enough votes to offset Mitt Romney’s strength elsewhere in the state -- especially the southwestern corner including Cincinnati and its suburbs.

In 2008, Obama won Ohio base in part on his large margins in Cuyahoga, where 61 percent of registered voters cast ballots. With only a few hours before the polls close at 7:30 p.m., Democratic officials are hoping to hit at least that turnout percentage again.

“When this gets north of 60 [percent], I’ll breath a little easier,” said county Democratic Chairman Stuart Garson. “I’d like to see it cross 70” percent.