NEW BRITAIN, Conn. — Mounting a show of support from like-minded governors, President Barack Obama put a spotlight Wednesday on a minimum wage push that Democrats hope will appeal to economically squeezed voters in November’s midterm elections.

Standing at the center of a packed college gymnasium, Obama said raising hourly wages to $10.10 would pull millions of Americans out of poverty. While one of Obama’s top priorities, the proposal is more likely to serve as a rallying cry for Democrats in the approaching election than to be adopted by Congress in the foreseeable future.

In a nod to staunch Republican opposition, Obama urged Americans to demand answers from their lawmakers about whether they support raising stagnant wages and ask if not, why not?

“Ask them to reconsider. Ask them to side with the majority of Americans,” Obama said. “Instead of saying no for once, say yes.”

The backdrop as Obama rallied a crowd of 3,000 at Central Connecticut State University: Four Northeastern governors — from Connecticut, Massachusetts, Vermont and Rhode Island — who support Obama’s proposal.

More than 20 states have increased their state-level minimum wages, said Labor Secretary Tom Perez, including six in the year since Obama first called for a federal increase. Democrats believe the push will bolster a populist message about expanding opportunity that they believe offers their best shot at fending off Republicans this November.

As if to underscore how politically charged the issue has already become, Republicans seized on Obama’s appearance to accuse him of threatening to obliterate badly needed jobs.

Republicans cite a study from the nonpartisan Congressional Budget Office estimating the proposal would cut employment by roughly 500,000 jobs. The White House disputes that finding, while embracing another finding from the same report that says more than 16.5 million people would see higher earnings by 2016.

“The problem is Republicans in Congress oppose raising the minimum wage. Now I don’t know if that’s just because I proposed it,” Obama said to laughter from the largely supportive crowd. “Maybe I should say I oppose raising the minimum wage, and they’d vote for it.”

Poking fun right back, House Speaker John Boehner’s office released a parody “fact sheet” in the style typically used by the White House to outline Obama’s proposals.

The headline: “President Obama Offers Plan to Destroy Jobs for Low-Income Americans.”

“When folks are still struggling to find work in this economy, why would we make that any harder?” said Boehner spokesman Brendan Buck.

Outside the gymnasium where Obama spoke, a handful of protesters waved the Ukrainian flag in apparent solidarity with Ukraine’s new government, while immigration activists chanted: “Obama, don’t deport my mama.”

Obama’s visit to a state he handily won twice served as a nagging reminder than Obama is struggling to maintain the public’s support amid concerns about his health care law and a still-sluggish economic recovery. Just 45 percent of voters here approved of the president — his lowest score in Connecticut — according to a Quinnipiac University poll released this week.