Midterm elections that will decide control of the Senate are three months away, and the 2016 presidential campaign will start in earnest soon after. Yet the Republican Party still hasn’t figured out what to do about illegal immigration.

It’s the issue that vexed Republicans as much as any in their 2012 presidential loss. It’s the one problem the party declared it must resolve to win future presidential races. And it managed to bedevil the party last week, when House Republicans splintered and stumbled for a day before passing a face-saving bill late Friday night.

Friday’s events proved anew that a small number of uncompromising conservatives have the power to hamper the efforts of GOP leaders to craft coherent positions on key issues.

“It would be very bad for Republicans in the House not to offer their vision of how they would fix the problem,” South Carolina GOP Sen. Lindsey Graham said when the initial House bill on immigration collapsed. While Republicans in the House are able to reject the proposals of Democrats, Graham said, that’s not enough: “At least they have a vision.”

While often a flashpoint issue among Republicans in their primaries this year, the party could get a grace period of sorts in November. Immigration appears likely to have only a modest impact on the roughly 10 Senate races that will determine control of the chamber. The possible exception is the race between Democratic Sen. Mark Udall and GOP Rep. Cory Gardner in Colorado, where Hispanic voters made up 14 percent of the electorate in 2012.

Senior White House adviser Dan Pfeiffer said on ABC News’ “This Week” on Sunday that President Barack Obama will make a decision by the end of the summer on how to use his authority to address immigrants living illegally in the U.S.

He said Obama is waiting for recommendations from Attorney General Eric Holder and Homeland Secretary Jeh Johnson before taking action, but any actions would be within “the confines of the law.”

Whatever Obama decides, Democratic strategists say Republicans won’t reap much of a benefit. Republicans, they argue, have already squeezed as much as they can from voters angry at the president by hammering at his record on health care, the IRS, foreign policy and other issues.

“There’s a ceiling, and nothing the president can do can get them above the ceiling,” said Rep. Steve Israel of New York, head of the Democrats’ efforts to win House elections. “But swing voters and persuadable voters, they want solutions.”

Hispanics made up less than 3 percent of all registered voters in 2012 in seven other states with competitive Senate races: Louisiana, Arkansas, North Carolina, Iowa, Michigan, Georgia and Kentucky. So any Democratic benefits from an Obama executive action on immigration could be just as limited.

Both parties agree that immigration is likely to play a bigger role in the 2016 presidential election. Arizona Sen. John McCain, the GOP nominee in 2008, has said his party can’t win without supporting an overhaul of the nation’s immigration laws, while former Florida Gov. Jeb Bush is among the potential candidates to urge the party to liberalize its approach to immigration.