RACINE, Wis. — To Mitt Romney, the 10 electoral votes in Wisconsin may be more essential than extra, a critical backup plan if a first-tier battleground state falls out of reach.

Seven weeks until the election, with Mr. Romney facing new questions about his ability to gain trust among voters experiencing economic hardships, his campaign is increasingly pointing to Wisconsin as a place where a statewide Republican resurgence could rub off on Mr. Romney.

But President Obama has overtaken Mr. Romney on who would do a better job handling the economy, according to a new Quinnipiac University/New York Times/CBS News poll of likely Wisconsin voters. The poll also found that Mr. Obama has a 17-point edge over Mr. Romney when voters are asked if a candidate cares about their needs and problems.

As the president makes his first campaign visit of the year to Wisconsin on Saturday, the poll found that Mr. Obama was the choice of 51 percent to 45 percent for Mr. Romney among likely voters. The six-point lead, which includes those who said they were leaning in one direction or another, marks a slight shift in Mr. Obama’s direction since Representative Paul D. Ryan of Wisconsin joined the Republican ticket last month.