WASHINGTON — With a government shutdown deadline just days away, House Speaker John Boehner faces a fateful choice over whether to abandon conservatives to reach a final deal on 2011 spending.

If the Ohio Republican puts the priority on GOP unity, he could force a shutdown that many strategists believe could be costly to his party. But if he goes for a deal with Democrats, the decision has the potential to splinter the new Republican majority in the House. Either way, the choice could define his leadership.

At issue is the size of budget reductions that the Republicans are willing to accept for the rest of the 2011 budget year. Last week, in negotiations with Democrats, Boehner appeared to be ready to propose roughly $26 billion in cuts for the remaining six months of the fiscal year on top of $10 billion already signed into law.

A number close to that likely would be able to pass the Senate, where Democrats are still the majority, giving both parties a political victory at a time of heightened public concern over Washington spending.

But such a compromise is inadequate for the conservative House GOP wing, many of them newcomers who want deeper cuts and have cemented support from veteran Republican lawmakers.

Both sides say they want to avoid a shutdown, and Democrats are urging Boehner to get negotiations back on track. Late Monday evening, White House chief of staff William Daley called Boehner to try to bring the two sides back to the table.

“Speaker Boehner is caught between a shutdown and a hard place,” Sen. Charles Schumer, D-N.Y., said Tuesday on the Senate floor. “It’s time to forget the tea party and take the deal.”

To make matters even more complicated for Boehner, the influential Tea Party Patriots group plans to stage a rally at the Capitol on Thursday.

“We think we should push for $90 billion in cuts,” said Mark Meckler, co-founder of Tea Party Patriots.

Boehner has succeeded so far in holding his conference together partly because the votes he was asking members to take were more matters of political symbolism than actual consequence.

But the spending issue strikes at the hearts of many rank-and-file members who ran their campaigns on a promise to end Washington’s profligate ways. In deeply Republican districts, their voters want to cut more deeply.

Any deal prompting more Republicans to defect would push Boehner into further dependence on Democrats.

Democratic leaders in the House indicated Tuesday that they would be willing to help pass a budget measure. But for Boehner, allies like those would only further reduce his standing among conservatives, both in and out of Washington.

“That’ll be the challenge for Boehner,” said Ronald Peters, a political science professor at Oklahoma University’s congressional studies center. “The only tool at his proposal now is his persuasion.”

Boehner showed his pragmatic side two weeks ago, when faced with a stopgap proposal to keep government running.

That measure, which expires April 8, cut federal spending at a rate on par with the earlier House-passed bill of more than $61 billion, one of the largest one-time reductions to domestic education, arts, health and infrastructure programs of its kind.