A debate over how to respond to California’s new Congressional map has deeply split the state’s GOP delegation and is pitting two top-ranking Members — Majority Whip Kevin McCarthy and Rules Chairman David Dreier — against each other in the fight.

At issue is whether Republicans should pursue a referendum to put the new district lines, which could jeopardize as many as a half-dozen of the 19 GOP-held seats, before voters.

Adding to the drama is a mystery: a lawyer filed paperwork on Aug. 30 in California to pursue the referendum, but at a lunch meeting Thursday to discuss the issue, none of the Republican Members said they were behind the effort.

“Nobody’s really raising their hand, so if you can find that out, let me know,” one lawmaker said. “Everybody’s denying that they’re the one doing it.”

The question boiled over in August during a delegation conference call that devolved into finger-pointing and ended without resolution, according to three California sources with firsthand knowledge of the call.

The delegation “is at war,” one of the sources said.

Dreier and Reps. Elton Gallegly, Ed Royce and Gary Miller want to pursue the referendum and oppose the new district lines, these sources said. McCarthy and Reps. John Campbell, Dana Rohrabacher and Buck McKeon are against it.

Of course, the new district lines affect each of the California Republicans differently.

According to charts put together by Ron Nehring, a former chairman of the California Republican Party who is backing the referendum push, McCarthy’s redrawn district would become slightly more Republican — giving him a safe seat with a nearly 20-point registration advantage.

Dreier’s district was essentially obliterated under the new lines drawn by a bipartisan commission, leaving him with few options if he wants to seek re-election. The voter registration of his new district is nearly 24 points more Democratic than his current swing district, giving Democrats a 19-point advantage.

McCarthy was particularly exercised in his opposition to the referendum on the August conference call, sources said.

“I didn’t come down hard on anybody,” McCarthy said in a brief interview. When told about others’ description of him being angry, McCarthy said, “Hmm. That’s odd,” before departing into a closed-off corridor.

Dreier, through a spokeswoman, declined to comment.

Gallegly and Reps. Jeff Denham and Dan Lungren also took significant hits in their district’s GOP registration numbers under the new lines.

Royce and Miller now share a district, forcing them to compete against each other.

The GOP registration increased by relatively small margins in the districts held by Rohrabacher, McKeon and Campbell.

The debate about whether to pursue the referendum is far more complicated than simple self-interest, however.

To challenge the redistricting plan, petitioners would need to file more than 500,000 signatures by Nov. 15, according to a timetable prepared by Dave Gilliard, a prominent Sacramento-based Republican consultant.

Obtaining the signatures in time would be expensive, and the California delegation has dismissed an earlier suggestion of seeking money from the National Republican Congressional Committee to pay for the effort.

California officials are still determining the House ethics and Federal Election Commission rules for raising funds for the signature drive, complicating the matter further.

And even with the signatures and passage at the ballot box in November 2012, the outcome would remain unclear.

After signatures are verified, the commission plans would be on hold until after the 2012 elections, Gilliard wrote in his analysis.

“The Supreme Court hires special masters to draw lines for the 2012 election,” he wrote. If the referendum passes, “the Court lines stay in effect for the decade. If the referendum fails, the commission lines go into effect in 2014.”

The referendum could be next June or November, California sources said.

Despite their prospective loss of several House seats in California, some Republicans are relieved that the results won’t be worse in the Democratic state. They note that the bipartisan redistricting plan approved in 2001, which protected the political status quo, helped Republicans prevent the alternative of losing as many as five seats if Democrats had drawn that plan.

Since the 2002 elections, only one House seat has changed party control — the northern California seat that Rep. Jerry McNerney (D) won in 2006 by unseating then-Rep. Richard Pombo (R). And since then, GOP political clout has continued to weaken statewide. California was notably absent from last November’s nationwide Republican sweep, despite having big-spending gubernatorial and Senate nominees.

Based on the state’s spicy redistricting history, a plan drawn by the state Supreme Court likely would jeopardize incumbents in both parties and create several swing districts in the 53-seat delegation. A court review could also weigh arguments of whether the commission has been sufficiently responsive to minority interests under the 1965 Voting Rights Act or relevant state laws.

Another twist in the debate is that for Members who supported establishing the redistricting commission in the first place, it’s difficult to oppose the commission’s new lines.

“I very strongly supported the initiative that set up this commission,” Campbell said. “I don’t think they did that great a job either, but they did a heck of a lot better job than the Legislature would have done. … I think it’s difficult to have set up this commission and turn around [and oppose it.]”