The lopsided number of Democratic votes against the war funding bill has House liberals worried about how often Speaker Nancy Pelosi will cut centrist deals, leaving the liberal base out of the loop on policy decisions.

The agreement to provide $120 billion in funding for the Iraq War and other initiatives (HR 2206) advanced despite the opposition of 61 percent of House Democrats, including Pelosi, D-Calif.

It wasn’t a total White House blowout — Democrats got the minimum wage increase they very much wanted, and they structured the legislation to force a showdown on another war spending measure in September. Because of that, Pelosi won broad praise from several corners of her caucus for making a tough strategic decision.

But there’s grumbling in other corners.

Some senior lawmakers, among them Jerrold Nadler, D-N.Y., said Pelosi should have polled fellow Democrats before deciding when and how to move important bills, especially the pending free trade deals with Peru and Panama.

Voters will be confused about what Democrats believe in, he said, if the party advances bills that most Democrats do not support. “You tell voters you’re going to do things. If those things don’t get done . . . nobody knows who to blame. And the electorate gets to be cynical and alienated,’’ Nadler said.

“We should not put a bill on the floor that the majority of the majority party is going to vote against,” he said. “Or at least, we should not move these bills unless the majority of the majority decides we should move them.”

Nadler is not alone.

A member of Pelosi’s leadership team said, “A number of Democrats are now calling for a ‘majority of the majority’ rule on the issue of free trade.

“The vote on extending funding for the war created a great deal of anxiety and put stress on the caucus,” that senior Democrat continued. “People are concerned that it will set a precedent. They are asking whether this will occur on other issues.”

The concept of bringing to the floor only bills that have the support of most members of the majority party was one of the governing tenets of former House Speaker J. Dennis Hastert of Illinois when Republicans controlled the chamber.

“There’s a reason why we had the majority of the majority rule,’’ said House GOP Leader John A. Boehner of Ohio. “That kind of rule is important to define your party and where your party is relative to the American people.”

Suggestions that Pelosi follow the GOP’s lead in that respect do not sit well with the new Speaker. “I’m the Speaker of the House. I have to take into consideration something broader than the majority of the majority,” Pelosi told reporters May 25.

Pelosi said she intends to “work in a very collaborative way,” but said her choices would be based on her judgment and her institutional role.

Even on the bedrock issue of free trade, the Speaker declined to offer the caucus a majority-rules position. “I don’t think that that’s going to be the case,’’ Pelosi said.

Instead, she said she would back efforts by Ways and Means Chairman Charles B. Rangel, D-N.Y., to develop free trade deals with Panama and Peru that match the principles outlined in a recent bipartisan deal with the White House and GOP leaders. That deal requires the Bush administration to try to insert enforceable, internationally recognized labor and environmental standards to pending trade pacts before Congress takes them up.

“I would encourage my colleagues not to be proposing resolutions that say the majority of the majority,” Pelosi said. “We have to talk it out, see what is possible to get the job done.”

Former Democratic Rep. Martin Frost of Texas (1979-2005), said Pelosi might need that flexibility on trade and immigration.

“She should not be bound to making decisions based on a nose count. She needs to do what’s in the best interest of the country,” he said.

“But,” he cautioned, “a leader that goes against their caucus too often won’t get elected in the next Congress.”