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Mr. Romney is also facing a small but steady drumbeat of conservatives from former Mississippi Gov. Haley Barbour to Texas Gov. Rick Perry calling for him to release more of his tax returns in an effort to combat Democrats’ implications that he must have something to hide. He has released his 2010 tax records and an estimate for 2011, showing that he paid an effective tax rate of about 14 percent in 2010.

However, Rep. Marsha Blackburn, Tennessee Republican, said voters she is talking to simply don’t care about the issue.

“When it comes to tax returns, it is my understanding that the governor has released the same number of tax returns at Sen. [John] McCain” in 2008, she said. “Quite frankly, what the American people are talking about is not tax returns — it’s jobs and the economy.”

Mr. Romney’s trip to Ohio comes just days after Mr. Obama swung through the state, which will certainly receive ample attention from both sides: No Republican presidential candidate has ever lost Ohio and won the White House. Real Clear Politics’ latest average of polls has Mr. Obama leading by 3.8 points in the state, which he won by 4 points in 2008.

Mr. Obama’s campaign, in concert with the Democratic National Committee and the Ohio Democratic Party, has also sued the state’s chief election official over a new law that curbs in-person early voting in the three days before Election Day. The lawsuit argues that most residents are unfairly treated, since the law exempts overseas and military voters. The move is the latest in an ongoing battle between Mr. Obama and Republican states that have recently passed new voting laws. Proponents of the laws, some of which require photo identification at the polls, say they are intended to curb voter fraud, but opponents claim they are thinly-veiled attempts to suppress Democratic turnout.