The bipartisan budget deal might have a tougher time passing than Republican or Democratic leaders first thought.

Although House Minority Leader Nancy Pelosi, D-Calif., said Thursday that she didn’t think her members would “let this bill go down,” she also said Democrats are likely to vote against the rule — the procedural vote that brings the bill to the floor.

If that’s the case, and Democrats remain unified in that effort, it won’t take many in the GOP to sink the rule.

There are many more than 20 Republicans who hate this deal. A group of them assembled at a monthly “Conversations with Conservatives” event Wednesday, where Rep. Raúl R. Labrador, R-Idaho, said the only part of him that was “undecided” on this vote was “whether I’m a strong no or a really strong no.”

”I think it’s a terrible plan,” he said.

Indeed, plenty of conservatives — who have exhibited willingness in the past to play politics with the procedural rule vote — are wondering what’s in this deal for them.

To make matters worse, those Republican members are frequently in contact with the outside conservatives groups that Speaker John A. Boehner, R-Ohio, has blasted for two consecutive days. And given the news releases and Twitter fights, conservative groups such as Heritage Action for America abhor this deal and GOP leadership more than ever before. (To make matters even worse, a top conservative staffer beloved by the groups was forced to resign Wednesday amid charges that he was leaking member-level conversations to the groups.)

If the conservative groups and the band of Republicans can mount a speedy offensive, they can sink the rule, and, potentially, the budget deal.

For Democrats, there’s a calculated risk in allowing that to happen. On one hand, this is probably just about the only budget deal they’re going to get. Allowing it to go down could prevent any sort of relief from the sequester. On the other, if Republicans need help on the rule, Democrats might — just might — be able to extract some other legislative concessions, and tops on their wish list is an extension of unemployment insurance.

Democrats have made it clear that the absence of an unemployment insurance extension is a major issue for them. Pelosi herself has issued less than lukewarm words on the deal because it does not include it.

Boehner has signaled that Republicans could be open to dealing with that issue separately from the budget, but he has made no firm commitment. Democrats, meanwhile, are insistent Congress extend the benefits.

On Thursday, Pelosi said she didn’t “even think it should be paid for,” a reference to the Republican insistence that such an extension have an offset.

Either way, the rule is due up for consideration on Thursday afternoon. It’s an open question how it plays out. Will Republicans be able to pass the rule on their own? Will any Republicans break from their ranks? Will Democrats help at all? And what might the legislative implications be if Democrats have to help?