And once again, the debate is centering on whether the RINOs are simply doing what they need to do to avoid becoming an endangered species.
Having lost several of their key members either at the polls last November or because of retirement, the moderates, who prefer their Tuesday Group moniker to the RINOs acronym, are searching for their role in the new Democratic-controlled House.
Here's the rub: They want to return the GOP to the majority. But the Democrats have pushed several bills that they favor and, more importantly, that their constituents -- mostly from the Midwest and Northeast -- want them to support.
Moderate Republicans have insisted for years that they have had to cast votes that might run contrary to their traditional Republican districts if they want to get reelected. And they can point to the losses of senior members such as Rep. Nancy Johnson (R-Conn.) last year to back up their arguments.
Many of the moderates supported the early Democratic bills, including a boost in the minimum wage. And if history is a guide, a number of them can be counted on to support efforts to increase domestic spending during the upcoming appropriations battles. And a few got a tremendous amount of publicity when they recently visited President Bush to give him some of their unvarnished counsel on Iraq.
The loyalty of Tuesday Group members was questioned last week during a House GOP conference, when Rep. Scott Garrett (R-N.J.), a member of the conservative Republican Study Committee, questioned why several Tuesday Group members voted for a Democratic gasoline price gouging bill.
"It was pointed out that we could have beaten back that bill if we had voted a different way," said Rep. Ray LaHood (R-Ill.), a member of the Tuesday Group. But LaHood said it would have been tough to go back home to Illinois -- where gas can be more than $3.50 a gallon -- if he had voted the way conservatives wanted.
Another moderate Republican acknowledged that he feels freer to vote the way he wants now that Democrats are in charge. In the past, Republican leaders would push for Republican unity to pass bills. "You don't feel as constrained," said Rep. Mike Castle (R-Del.).
And that lack of constraint is likely to play out as Congress starts the appropriations process. Last year, a group of moderates pushed increases in health and education spending, and Castle already has signaled that he will mount a similar effort this year.
In public, the moderates say that they and the Republican Study Committee members are getting along fine. And they point out that even outside groups associated with their wings of the GOP -- the moderate Republican Main Street Partnership and the conservative Club for Growth -- have tried to make peace. "We realize we're all in the minority," said Rep. Fred Upton (R-Mich.). "The long knives have been put away."
Republican Study Committee Chairman Jeb Hensarling (R-Texas) declined to directly discuss the moderates and their votes. "I am concerned every time someone votes a different way than I do," he said. "I would hope that most Republicans would conclude that what unites us is more important than what divides us."
He said that Republicans must offer voters a clear message, adding, "Our goal will not be achieved if it's every man or woman for him- or herself."