WASHINGTON—Voters in a swing state went to the polls for the first time Thursday to cast ballots in the general election, as both presidential campaigns sought to capitalize on an early voting process that will soon be underway in more than half the country.

In Iowa, the first swing state to open the polls, voters were lined up to cast their ballots from a Mexican grocery store in Denison to the county auditor’s offices in Des Moines and Davenport.

Analysts said the early voting—in which voters can petition for satellite polling sites in their counties or take advantage of the more traditional form of mail-in ballots—could give an advantage to President Obama, who is leading former Massachusetts Governor Mitt Romney in the polls and has a more extensive grassroots organization than his Republican challenger.

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Specialists predict that more early voting will take place this year than in 2008 – with as much as 35 percent of the total vote cast well before election day on Nov. 6, including many before the three presidential debates scheduled for next month.

The Obama campaign appeared to be making a more aggressive effort in Iowa, where the president won his first presidential contest during the 2008 Iowa caucus and prevailed over Senator John McCain by nine percentage points in the general election.

Nursing student Kim Boggus, 33, who volunteered for Obama in 2008, was one of the first batch of Obama voters who showed up at the Polk County auditor’s office in Des Moines.

“We got together for coffee and spoke about the importance of taking advantage of these 40 days,” she said by telephone. “We’re going to spend the next 40 days knocking on doors and calling people.”

While Romney is expected to do well in Iowa’s rural areas, Boggus said the Des Moines polling station had taken on the feel of an Obama campaign rally.

“There was not a single Romney person. There was cheering, we were taking photographs. Everyone was fired up and ready to go to cast votes for Obama,” Boggus added, referring to one of the president’s signature lines during his first run four years ago.

“Close to 200 people” were lined up before 8 a.m., Erin Seidler, the Obama campaign’s Iowa communications director, said early Thursday of the main Des Moines polling site.

Obama’s re-election campaign takes pride in having an extensive get-out-the-vote effort in the Hawkeye State, where the president has 67 field offices compared to Romney’s 14. Not all polling places open early—voters petition for sites in their areas.

In Linn County, home to Cedar Rapids, Obama supporters petitioned for early polling stations at a union hall, on three college campuses, and at an African American church.

The Obama campaign is also enlisting actor Jason Alexander, of “Seinfeld” fame, to help roust voters in Iowa. Alexander is scheduled to visit four polling sites Thursday in Neveda, Des Moines, Adel, and Winterset.

Romney supporters, meanwhile, have petitioned for early polling places in more friendly territory such as Lutheran churches and his campaign expressed confidence that they will contest the state.

Romney campaign spokesman Shawn McCoy told the Associated Press that the former Massachusetts governor’s supporters are making sure there are early voting locations “so that more Iowans have an opportunity to voice their support for Gov. Romney.”

Romney has visited the state six times and spent an estimated $8 million on ads criticizing Obama’s record in a bid to win Iowa’s six electoral votes on Nov. 6.

Early voting will take place in 32 states nationwide over the next few weeks, including six of the nine most contested battlegrounds. More than 44 percent of the electorate will have the opportunity to vote early. In 2008, according to the Obama campaign, a majority of ballots were cast early in Florida, North Carolina, Nevada, and Colorado.

Both campaigns see the early voting effort as a way to free up their most active supporters to volunteer on election day. Several Obama campaign officials also said they hope that with the president now up in most polls in Iowa and other battleground states, convincing citizens to cast early ballots could also neutralize any plans by the Romney campaign to blanket the airwaves with negative ads in the closing weeks of the campaign.

First Lady Michelle Obama, who has been a key surrogate for her husband, is scheduled to hold a rally Friday at the University of Northern Iowa in Cedar Falls.