Speaker John A. Boehner’s decision to allow a bill to pass with only 49 Republican votes Tuesday has some in his party questioning whether this is the new normal and has at the same time delighted Democrats, who believe they might be able to produce similar results in the battles ahead.

The Ohio Republican has generally operated under a policy of bringing bills to the floor only if a majority of his conference can support it. But that was not the case on Tuesday night’s vote on supplemental disaster relief for those stricken by Superstorm Sandy, nor the fiscal cliff deal, which passed with only 85 Republicans on board earlier this month.

That has Republicans questioning whether the “Hastert rule” is dead.

“That rule is completely dead,” one Republican aide said. “The Democrats now effectively control the floor because nothing ‘big’ will come to the floor without knowing in advance that lots of Democrats support it. That gives the Democrats tremendous power in a body where the minority is not designed to have much power.”

In fact, the rule’s namesake, former Speaker Dennis Hastert, R-Ill., blasted Boehner earlier this month for bringing bills to the floor too often that turn off members of his own conference, holding that doing so empowers President Barack Obama and Minority Leader Nancy Pelosi of California.

“Maybe you can do it once, maybe you can do it twice, but when you start making deals when you have to get Democrats to pass the legislation, you are not in power anymore,” he said on Fox News Radio’s “Kilmeade & Friends.” “When you start passing stuff that your members are not in line with, all of a sudden your ability to lead is in jeopardy because somebody else is making decisions. The president is making decisions, Pelosi is making decisions, or they are making the decisions in the Senate.”

House Republican leadership, however, contends that those two votes were extraordinary circumstances. The fiscal cliff vote involved the perception that taxes would be raised, which scared off many Republicans. When it came to Sandy aid, the overwhelming public pressure, including from New York and New Jersey GOP officials, made it impossible not to bring the bill to the floor.

“The fiscal cliff legislation and aid to Sandy were very particular circumstances,” a GOP leadership aide said. “Everyone has been very clear that the goal is to proceed in regular order and with as many Republican votes as possible because that leads to the best policy.”

The point is sure to come up this week as House Republicans meet in Williamsburg, Va., for their annual retreat. Still, even some Republicans who did not vote for Boehner during the failed attempt to mount a coup against his leadership earlier this month were thinking positive ahead of the retreat.

“I think he can hold the conference,” said Rep. Raúl R. Labrador, R-Idaho, one of the Boehner detractors. “As Boehner said, he’s going to work with the conference to make sure we can get the most conservative bills out of the House, and I trust that he will do that.”

Similar battles are on the horizon. The debt ceiling, the sequester and a continuing resolution must be dealt with in the next three months, and it remains to be seen if Boehner can out-maneuver Democrats in a way that will allow him to carry most of his conference.

Furthermore, Senate Democrats have pledged to bring up gun control legislation this month and an immigration overhaul soon after, and Obama is looking to re-create the circumstances that allowed him a Democrat-friendly fiscal cliff deal.

House Democrats, for their part, are cheering the weakened position Boehner has found himself in. Rules ranking member Louise M. Slaughter, D-N.Y., pointed to the near-Democratic unity on the Sandy votes and the fact that Republicans did not allow some potentially killer amendments on the bills as proof positive that House Democrats are empowered in the 113th Congress.

“I’m not sure they can pass anything without us. I love it. That means we can negotiate for a change,” she said.

Rep. Diana DeGette of Colorado, on the other hand, said it’s too early to say how powerful the minority will be, but the fiscal cliff bill showed that it might take Democrats to get legislation past the president.

“I think actually the fiscal cliff experience has taught the Republican leadership that if they really want to pass sane legislation, they are going to have to work with us,” she said. “And we are eager to work with that.”

DeGette said that’s particularly true of bills such as appropriations, which have to get done to keep the government operating, and noted the Sandy bill as another example.

She’s also hopeful that Democrats will be able to convince the GOP to allow some of the president’s other proposals to move, including gun legislation.

“I think we can get the magazine part done,” she said, referring to high-capacity ammunition magazines. “Take a look at the polling.”

While Boehner’s inability to control his conference undoubtedly gives Pelosi more leverage than expected, there are still limits to her power.

In the fiscal cliff talks, for instance, she played a bigger role than she had in any of the other fiscal negotiations in the 112th Congress. But her power was still relatively modest, with Vice President Joseph R. Biden Jr., Obama and Reid taking the lead.

Specifically, Pelosi fought to keep Obama from putting a change to the Medicare eligibility age on the table, and Obama went over the details of the deal with Pelosi after it was agreed to but before it had been announced.

On the other hand, Pelosi was forced to strongly back another entitlement reform loathed by liberals, a change in how Social Security payments increase with inflation called “chained CPI,” when Obama considered accepting it as part of a deal.

Steven T. Dennis and Jonathan Strong contributed to this report.