Senate Finance Chairman Chuck Grassley (R-Iowa) and House Ways and Means Chairman Bill Thomas (R-Calif.) are fighting again, and this time both the child tax credit bill and the Medicare prescription drug bill are caught in the crossfire.

The lawmakers are at odds over who should preside over the conference committee to reconcile the Senate’s bill to send $400 tax rebate checks to low-income families with a broader House bill.

“I don’t see why they get so persnickety about it,” said Sen. Trent Lott (R-Miss.), who will likely be a member of the conference committee. “It’s probably pretty obvious which one of them should chair the conference, but I guess they don’t want to do that, so they can chair the Medicare conference.”

Indeed, the dispute stems from a larger debate over which of the two chairmen will preside over the conference on the Medicare prescription drug benefit bill — differing versions of which are expected to pass both the House and Senate before Congress leaves for the July Fourth recess.

To get around the dispute and avoid a protracted fight over the additional tax cuts included in the House child credit bill, Grassley is toying with simply sending the Senate’s bare bones child tax credit bill back to the House, in the hopes that White House support for it might compel House leaders to act. If that version passed through the House, there would be no need for a conference.

But one House GOP leadership aide warned that such a strategy would likely backfire on the Senate and the White House.

“I think our history shows we won’t bend to that pressure,” said the GOP aide, who noted the House leadership may even decide to bring the Senate version to the floor just to kill it.

House GOP leaders already blame Grassley for giving the issue extra life by heeding what they see as partisan-driven Democratic demands to restore the low-income family tax rebate checks, which were eliminated from President Bush’s $350 billion tax-cut bill during conference negotiations last month.

So when the House passed their version of the measure, they added tax cuts for families of astronauts who die on missions and members of the Armed Forces as well as extended the child tax credit for a longer period of time than the Senate would — as part of their strategy to attract GOP conservatives who complained the tax rebate checks would go to people who do not pay federal income taxes.

Grassley, who has the support of the White House, has balked at the $82 billion price tag of the House measure, because his slimmer bill would be paid for with increased passenger and customs fees.

But one Senate GOP leadership aide indicated that Grassley may not get the Senate leadership’s blessing to re-pass the same bill and send it back to the House. This aide said Senate leaders would likely advise Grassley to simply go to conference with the House — following the completion of the Medicare bill — rather than potentially causing more friction.

Because the panels’ traditions dictate that the two chairmen trade off as the chairmen of House-Senate conferences, Grassley has indicated that he believes it’s Thomas’ turn, because Grassley chaired the last conference on the president’s $350 billion tax-cut bill.

But Thomas has long had his sights set on chairing the prescription drug conference, the chairmanship of which, if Thomas was to chair the child tax credit conference, would fall to Grassley.

Given that the $350 billion tax cut and the Medicare prescription drug measure are the most high-profile measures to come out of both panels this year, Ways and Means members offered support for Thomas and noted that the two chairmen had agreed some time ago to split the leadership of the conference committees on the two measures.

“The idea was that Chairman Grassley would handle the first conference and Chairman Thomas would handle the second conference [on Medicare],” said Rep. Rob Portman (R-Ohio). “It just made sense to divide it up that way.”

Rep. Jim McCrery (R-La.) agreed, but noted that the House and Senate leaders would likely have to intervene to settle the dispute.

“It’ll be a joint House-Senate leadership decision on who will chair the conference,” said McCrery. “But I think the Senate is going to chair the conference on the child tax credit because it’s an extension of the previous bill.”

Indeed, Thomas appears to resent Grassley’s assumption that Thomas should chair the child tax credit conference, because he vigorously argued for a $380 billion tax-cut bill that would have included the low-income family rebate checks. Grassley told Thomas he could not accept the $380 billion bill because moderate Republicans in the Senate were refusing to support any bill that cost more than $350 billion.

But one Senate GOP aide said the rotation should carry on regardless of which bill comes first.

Still, most Members said the dispute over conference chairmanships was a bit confounding given that both men are from the same party and chairing the conference only gives one the power to hold the meetings on his side of the Capitol and control meeting times.

“I don’t think it makes that much of a difference,” said Lott, who noted that former Finance Chairman Bill Roth (R-Del.) and former Ways and Means Chairman Bill Archer (R-Texas) also fought about conference chairmanships but “not quite as vigorously as these two do.”

Sen. Max Baucus (D-Mont.) agreed, but indicated the situation was unavoidable in some ways.

“It’s something you women wouldn’t understand,” Baucus said to a group of female reporters. “It’s a macho thing. It’s a male deal.”