Speaker John Boehner’s demand that any new debt ceiling hike be offset with spending cuts is already being met with grumbling from some in his Conference who believe the cuts promised in exchange for the last debt ceiling increase have not been realized.

And with Democrats openly questioning whether they can trust Boehner to negotiate in good faith — they accuse him of reneging on last year’s Budget Control Act — it remains unclear who in the House could give the Ohio Republican the votes he needs to pass a deal to increase the debt limit.

Boehner told reporters Wednesday that his announcement Tuesday was meant to spur action.

“We have time to deal with our problems,” he said. “What I’m trying to do is encourage people on both sides of the aisle, on both sides of the Capitol and on both sides of Pennsylvania Avenue to be honest with the American people, to be honest with ourselves, to begin to tackle this problem in an adult way.”

The fact that Boehner said he would not consider a debt limit increase without equal or greater spending cuts or reforms is hardly unexpected. With the makeup of his Conference, Boehner almost certainly could not pass a straight debt ceiling increase with a majority of Republicans. Such a bill was resoundingly defeated in the House last year.

Still, when Boehner struck the BCA compromise with Democrats, 66 House Republicans voted against it. If Boehner hopes to pass a debt limit increase without having to rely on Democrats this year, GOP leaders must adjust their strategy and convince at least some of those naysayers that real cuts will come.

As one of those “no” votes, Rep. Tim Scott said he will repeat his vote if he doesn’t see something different.

“Increasing the debt ceiling without any major reforms to how we’re spending money really didn’t make a lot of sense to me,” the South Carolina Republican said. “We’ll see what happens, but if it is what it was last year, then I’ll be doing what I did last year.”

Rep. Jeff Landry, who also voted against the BCA, said Wednesday he’s unconvinced that Boehner can deliver real cuts, especially because the Joint Committee on Deficit Reduction failed and the House is trying to replace the sequester’s automatic cuts that the committee’s failure set in motion.

“Those comments were the same comments I heard last year. I hope this time he means it,” the Louisiana Republican freshman said. “We just voted last week to undo what they created, so I don’t know. … Action speaks a whole lot louder than words.”

He said he would like to see a debt limit increase accompanied by a balanced budget amendment to the Constitution. The conservative Republican Study Committee, meanwhile, a group that Landry belongs to, has an updated “Cut, Cap and Balance” bill they might push.

South Carolina Rep. Mick Mulvaney, another Republican who voted against the BCA, said that would be his preferred option.

“We all voted for ‘Cut, Cap and Balance.’ I was glad it was embraced by leadership,” he said. “The framework is there. Maybe we should be looking at that as a guide to proceed to the next level.”

Boehner’s allies, though, say the group might be asking for too much.

“There are folks here who want to do a lot more a lot quicker,” Rep. Patrick Tiberi (R-Ohio) said. “But the Speaker is living in [the] reality of dealing with a Senate that’s controlled by Democrats and a president who has different ideas.”

There are some indications that GOP leaders can win over at least some of their Members. Rep. Trent Franks, who voted against the BCA, said he agrees with Boehner’s sentiment but not the strategy he used last year.

“Maybe some of us didn’t agree with the strategy that was used, but the impulse for it was certainly understandable. And he hasn’t changed his principle perspective. He may change his strategy, but the principle is the same,” the Arizona Republican said.

With all that, it remains unclear what strategy Republicans will pursue.

But either way, Democrats might be harder to convince to supply votes to the Speaker than they were last year. They said that Republicans reneged on the BCA when they passed the House GOP budget this year, which calls for cutting spending below what the agreement forecast.

House Minority Leader Nancy Pelosi (D-Calif.) told reporters that the Speaker’s demands are “irresponsible” and “immature.”

House Minority Whip Steny Hoyer, meanwhile, who would likely be tasked with negotiating for Democratic votes on a debt limit increase deal, said he wants to reach a bipartisan compromise but is concerned that Republicans went back on the BCA.

“I’m concerned that we had an agreement, we reached an agreement on the BCA, and the Republicans, in my view, have abdicated on that agreement,” the Maryland lawmaker said.

Similarly, Democratic Caucus Vice Chairman Xavier Becerra said the party’s trust level is low with the GOP, indicating negotiations could be tough.

“I think it’s difficult to trust the House Republican leadership when they have broken their own agreement and they have walked away from their commitments on more than one occasion,” the California lawmaker said.

Jonathan Strong contributed to this report.