WASHINGTON — There could be little President Barack Obama can do to find common ground with Paul Ryan, given their deep ideological differences and House conservatives’ inevitable demands for the speaker-in-waiting.

With Ryan’s announcement he will seek the House speakership, all eyes now turn to the Wisconsin Republican’s ability to manage his fractious caucus and find just enough common ground with a president many conservatives revile.

Ryan will have little time to settle in because of some fast-approaching fiscal deadlines. Congressional leaders must find a way in coming weeks to avoid a debt default and then see if they can strike a long-term budget deal.

But it is unclear how Obama and Ryan will resolve fundamental differences, including defense and domestic spending caps. House Republicans want any year-end budget deal to boost defense spending; the president is holding firm he will sign such a plan only if it includes an equal domestic spending increase.

“The Ryan-Murray (budget) compromise did allow spending in excess of what would have been permitted on both fronts,” said William Galston, a former administration official for President Bill Clinton. “Is Congressman Ryan prepared to accept, however grudgingly, the terms of spending symmetry?

“I don’t think the president will go along with asymmetry and demonstrated that with his veto,” Galston said in reference to a Pentagon policy bill would have authorized $38 billion in additional fiscal 2016 Pentagon spending.

Some Republican lawmakers believe such moves are illustrative of a White House unwilling to compromise. House Natural Resources Chairman Rob Bishop, R-Utah, said Ryan faces an uphill climb.

“The question should be, ‘can anyone work with this White House?’” Bishop said.

At the White House, the message about Ryan’s likely speakership and a new era of Obama-congressional deal making is measured.

White House press secretary said last week Obama has been “quite clear that he respects Paul Ryan” as someone “who obviously has spent a lot of time seriously thinking about some of the significant challenges facing the country.”

But Earnest’s remarks also made it clear the president and the presumptive House leader are members of different political parties with many divergent views.

“At the same time, the president has profound and occasionally vigorous disagreements with him on fiscal issues and presumably other things too,” Earnest said.

The well of Ryan-Obama legislative partnerships is shallow.

Many lawmakers and experts point to the budget deal Ryan struck with Sen. Patty Murray, D-Wash., in 2013 as an example of his ability to work with Obama. While he didn’t negotiate that plan directly with the president, Obama blessed it and signed it into law.

Several lawmakers, Republican and Democratic, also pointed to efforts Ryan made on an immigration overhaul in 2013 and a trade package Obama pushed through earlier this year as examples of cases in which the two have worked together.

On the trade legislation, Deputy House Republican Whip Tom Cole of Oklahoma said: “Not only did (Ryan) do it, he did that after being an opponent of the president. I thought it spoke highly of both of them, particularly Paul.”