What’s the Republican position on deporting 800,000 people eligible for the DREAM Act? The answer, according to Senate Minority Leader Mitch McConnell, is: They are waiting for presumptive GOP presidential nominee Mitt Romney to figure out his own position first.

“I think we’re going to wait until we hear what Gov. Romney has to say on this issue. … My view is he is the leader of our party from now until November and, we hope, beyond, and we’re going to wait and see what he has to say about it and be happy to respond to that at that point,” the Kentucky Republican said Tuesday.

But McConnell isn’t alone. Other Republicans are also uncertain about what to do about President Barack Obama’s shift last week to immigration policy. It’s an issue that has vexed Republicans for years, and as Obama no doubt hopes, it has the potential to cost them Hispanic votes and the election in November.

Republicans may be united in their concern about Obama’s unilateral decision Friday to stop deporting young illegal immigrants who might be eligible for the yet-to-be-passed DREAM Act. But that unity does not extend to what the GOP should do next. Immigration ripped Republicans apart when a comprehensive bill reached the Senate floor under President George W. Bush, and the new House Republican majority hasn’t shown an inclination to take on the issue either.

For Romney, the issue is also fraught with the potential for a major flip-flop. He used his opposition to the DREAM Act, which he has said he would veto, to help vanquish Texas Gov. Rick Perry in the primaries. Now facing a general election audience, Romney has been taking a more moderate tone — talking about a long-term solution for children brought here “through no fault of their own.” But he has yet to embrace a particular proposal or say they should not be deported.

The DREAM Act would provide a pathway to citizenship for illegal immigrants who came to the United States before the age of 16, have been in the country for five years, are younger than 30 and go to college or join the military. Obama’s order merely defers action for renewable two-year periods, during which eligible people could work. But the policy could be reversed by a future president. Romney hasn’t said whether he would reverse it.

Sidestepping the immigration issue itself, 20 Republican Senators wrote to Obama Tuesday evening questioning his authority to issue the DREAM directive. Led by McConnell, the group asked that the administration make several officials available to Congress, including Homeland Security Secretary Janet Napolitano, U.S. Immigration and Customs Enforcement Director John Morton and U.S. Citizenship and Immigration Service Director Alejandro Mayorkas.

“Please provide copies of any documentation, including any and all legal opinions, memoranda, and emails, that discuss any authority you have or do not have to undertake this immigration directive,” the Senators wrote. They asked to receive the documents by July 3.

The Senators note in the letter that Obama a year ago made statements indicating that he did not have the authority to carry out such an initiative.

“Why has your position on the legal authority of the Executive Branch changed,” the lawmakers wrote.

Still, the basic question of how to deal with illegal immigrants continues to bedevil the GOP as it seeks to court Hispanics while remaining a party that calls for the rule of law when it comes to immigration.

The most recent Republican effort on the DREAM Act has been led by Sen. Marco Rubio (R-Fla.), but he said this week he didn’t see a way forward after Obama’s action.

There may, however, be a move to breathe new life into the Rubio effort, lest the Republicans get painted into an anti-immigrant corner.

Sen. Jon Kyl (Ariz.) said it will be apparent in the next 48 hours if Republicans will put forward their own legislation. And McConnell pointed to a speech expected by Romney in front of Latino leaders on Thursday for guidance.

The 2008 Republican presidential nominee, Sen. John McCain (Ariz.), grew agitated as reporters pressed him Tuesday for what the GOP’s next move should be on the DREAM Act, given that the GOP has filibustered it in the past and Rubio has never made his own modified version public.

“The Republicans have shown, and Mitt Romney has shown, compassion and concern, for children who were brought here,” McCain said. “We need to address the issue and at the same time, the president has taken steps that just a year ago he said he could not take constitutionally.”

McCain said he’d be happy to see Rubio’s plan move forward.

“I would be glad to work on the issue, and most Republicans would be glad to work on the issue,” McCain said. “I have said all along that we need to address the issue.”

McCain said the immigration situation is Obama’s fault, given that he promised to take it up in his first year in office and has yet to propose comprehensive legislation. But the president and the White House have repeatedly and loudly called for Congress to act on DREAM, to no avail. And the Senate GOP led a filibuster of it in 2010’s lame-duck session after it passed the House and garnered 55 votes in the Senate.

Speaker John Boehner (R-Ohio), who said earlier this year that there wasn’t much chance of something like the DREAM Act making it through his chamber, also didn’t have an answer on what the GOP should do next, beyond saying that Obama’s making it harder by acting on his own.

“It puts everyone in a difficult position,” Boehner said. “I think we all have a concern for those who are caught in this trap, through no fault of their own are here. But the president’s actions are going to make it much more difficult for us to work in a bipartisan way to get to a permanent solution.”

Boehner said there is a question of whether Obama is violating the Constitution by acting without Congress, and he tried to pivot back to the economy.

Sen. Jim DeMint (R-S.C.) said that the president’s decision effectively poisoned the well for getting anything on DREAM or comprehensive legislation done this year.

“There’s no need to work through permanent legislation when the president’s done something,” DeMint said.

Senate Majority Leader Harry Reid (D-Nev.) ripped the GOP’s “phony outrage” over Obama’s action and said Republicans talk about the problem, but when the time comes to act, they find excuses. Reid said the Republicans are “taking their marbles and going home.”

Reid also knocked Romney for failing to say what he would do for days after Obama’s announcement.

“Romney’s had four or five days, and he was asked four different times on [“Face the Nation”] this weekend what he wanted to do, and he wouldn’t answer,” Reid said.

“He’s campaigned for a year and a  half. He should have some semblance, idea …[about] how he feels about that.”