COLUMBUS, Ohio — For weeks, Republicans in Ohio have been watching with worry that the state’s vital 18 electoral votes were trending away from Mitt Romney. The anxiety has been similar in Florida, where Republicans are concerned that President Obama is gaining the upper hand in the fight for the state’s 29 electoral votes.

Those fears are affirmed in the findings of the latest Quinnipiac University/New York Times/CBS News polls of likely voters in both states, which show that Mr. Obama has widened his lead over Mr. Romney and is outperforming him on nearly every major campaign issue, even though about half said they were disappointed in Mr. Obama’s presidency.

The polls, along with interviews with supporters and advisers in the nation’s two largest battleground states, lay bare an increasingly urgent challenge facing Mr. Romney as he prepares for his next chance to move the race in his favor, at the first debate with Mr. Obama next week. Mr. Romney’s burden is no longer just to win over undecided voters, but also to woo back the voters who seem to be growing a little comfortable with the idea of a second term for Mr. Obama.

As Mr. Romney arrived in Ohio on Tuesday for a two-day bus tour and the president was set to campaign here on Wednesday, the poll also found potential openings where Mr. Romney could gain support. More voters say he would be better than Mr. Obama at tackling the budget deficit — the only major issue where he had such an edge — and a majority agree with his assertions that the government is doing too much of what should be left to individuals and businesses.