It would mean undercutting their party leaders in the standoff with President Obama and Senate Democrats, and giving Democrats the power, for at least one vote, to set the agenda in the Republican-controlled House. But it might help end the government shutdown so many have decried.
Fitzpatrick, LoBiondo, and Runyan "will say anything to save their political skins and escape the blame for their shutdown, but when it comes time to put their money where their mouths are, they keep voting to block a clean budget resolution," said Marc Brumer, a spokesman for the Democrats' congressional campaign arm.
The same factors that may make the region's centrists more pragmatic than some of their peers, and key votes in any deal to end the shutdown - they represent districts where both parties' voters are well represented - also make them prime election targets in 2014.
So Democrats have blasted near-daily e-mails criticizing them as Republicans have balked at the Democrats' maneuvers.
A LoBiondo spokesman called those maneuvers "a procedural trick trying to be politically twisted and rebranded" as a clean spending bill. Fitzpatrick pointed out that the votes involve overriding rulings by the House's parliamentarian in an attempt to work around the chamber's rules.
Obama and Senate Democrats have insisted on a clean spending plan - one with no demands attached - to reopen the government, and with 20 or so House Republicans publicly supporting the idea in the name of ending the standoff, independent head counts show that the measure could win a majority and pass if breakaway Republicans joined with Democrats.
But House Speaker John A. Boehner has refused to bring the plan to a vote as he seeks concessions on the new health-care law.
Democrats, by their count, have tried nine times to override Boehner, and have planned a petition to force a vote on their spending plan.
At each attempt, Republicans - fractured over the shutdown strategy - have blocked Democrats with a unified vote, including those from the Philadelphia area.
They have quickly dismissed the petition, noting that the earliest it could bring about a vote is Oct. 28.
Runyan's "strong belief is that we need to reopen the government as quickly as possible," said a Runyan spokeswoman, "and a discharge petition simply would not do that."
The petition, a Gerlach aide wrote, "is more of the same hyper-partisanship that got us into this situation in the first place."
Indeed, the procedural moves are fraught with politics.
Supporting the maneuvers would require Republicans to help usurp their leaders' authority. LoBiondo said it would be akin to putting Democrats in charge of the House.
The moderates, in other words, have drawn a line between disagreeing with their speaker and undermining his control, especially on such a critical vote.
"The moment you begin to vote against your leadership, you've thrown open the possibility for cross-party coalitions or the minority party with dissident majority members to claim control of the agenda," said Sarah Binder, a political scientist at George Washington University.
Republicans who bucked their party in such a high-profile way could lose critical political support, including campaign fund-raising help. And though the moderates have argued over strategy, none has suggested deserting the party.
"They're Republicans, they're funded from Republicans," Binder said. "That's who they are, so there's a certain degree of intense loyalty to the speaker."
The Democrats' procedural gyrations have occasionally been successfully used by minority parties in the past, Binder said, though usually with far lower stakes than in the current showdown. Discharge petitions to force a vote have almost never succeed.
Each of the local lawmakers said he hoped to work out a bipartisan agreement to end the standoff, and all six have signed on to a plan spearheaded by Dent that would fund the government for six months and repeal an unpopular medical-device tax that helps fund part of Obama's health law, though that plan faces long odds.
The moderate lawmakers' pragmatism and adherence to the political chain-of-command stand in contrast to the House's rebellious tea party bloc, whose take-no-prisoners methods have allowed it to steer the House agenda.
Rep. Peter King of New York, who, along with Dent, is a leading voice of moderate Republicans and has called for a vote to end the shutdown, told the New York Times that he gives the tea party credit for backing up its words with action.
"They don't care what anybody thinks, and they don't care about bringing down the House," King said. Moderates, he said, "will complain, but they've never gone head-to-head."