"I really don't know the answer to that question. That is clearly in doubt," Ryan told ABC's "This Week" when asked if a reform package would make it to the president's desk this year.
"It depends on whether they're willing to actually secure the border, actually have interior enforcement, and agree to not having an amnesty," he said, referring to the Obama administration.
"If we can do that, where it's security first, no amnesty, then we might be able to get somewhere," Ryan said. "But I just don't know if that's going to be the case or not."
House Majority Leader Eric Cantor, R-Va., echoed Ryan's remarks, saying Republicans would support an immigration overhaul package, but only if it focused first on border security.
Both of them reflected a set of broad principles announced Thursday at a GOP retreat. The principles also call for legal status of immigrants living in or entering the United States illegally, but not citizenship, except "for those who were brought to this country as children through no fault of their own."
But Cantor said overriding the GOP principles was a fundamental lack of trust in the Obama administration.
"There's a lot of distrust of this administration and implementing the law," he told CBS' "Face the Nation."
"And we just heard the president in his State of Union address say, you know what? If he can't work with Congress, he's going to do it his own way. And that sort of breeds this kind of distrust. And I think we're going to have to do something about that in order to see a way forward on immigration," Cantor said.
"We don't think that we can allow this border to continue to be overrun," Ryan said.
"And if we can get security first, no amnesty, before anything happens, we think that's a good approach," he said.
"This is not a trust but verify; this is a verify-then-trust approach," Ryan said.
"Trust but verify" is a Russian proverb used by President Ronald Reagan during nuclear talks with the Soviet Union 26 years ago.
President Obama said in an interview broadcast on CNN Friday he was open to a plan that would initially give legal status short of immigration to many workers in the country without legal permission, provided they were not permanently barred from becoming citizens.
He separately said in an online town hall-style meeting Friday he was "modestly optimistic" an immigration deal could be reached this year.
He pledged in the online session he would look at all the options and said he would use his executive power if negotiations with Republican lawmakers broke down over the next several months.
The Senate passed legislation last June after Republicans and Democrats reached a compromise on a broad overhaul, but the House has not acted on it.