Hollywood central casting couldn’t have picked a better odd couple than a prairie pragmatist and a caustic Californian to battle over the right mix of tax cuts and carefully designed regional incentives to push President Bush’s economic growth plan through the House and Senate.

The White House and GOP Congressional leaders have put their collective faith in Senate Finance Chairman Chuck Grassley (R-Iowa) and House Ways and Means Chairman Bill Thomas (R-Calif.), whose infamous temper flared Wednesday as he walked out of talks with his Senate counterpart.

The clash is just the latest example of the difficulty for the chambers to find common ground when their lead negotiators are Grassley (the low-key, no-nonsense grain and livestock farmer) and Thomas (whose reluctance to compromise is well-known). This time, their task is to reconcile a Senate tax bill encumbered by a $350 billion ceiling and a House eager to enact as much of its $550 billion bill as possible.

“Their styles are very different,” said one GOP Senator. “ … They draw their lines in the dirt, and they generally stick to them.”

Because of their personality differences, not to mention the comparable sharp differences between the House and Senate tax bills, Members and aides say they keep a watchful eye on how Grassley and Thomas interact.

“There will be a lot of parental supervision,” said a Republican House Member of this week’s negotiations.

The tension came to a head Wednesday afternoon, when Thomas walked out of negotiations. Grassley had protested, according to a GOP source, Thomas’ announcement to the press earlier in the day that an agreement on a roughly $380 billion tax package had been reached. Grassley believed the publicity was a ploy to force the hands of wavering Senators, such as George Voinovich (R-Ohio) and Olympia Snowe (R-Maine), who have said they would not accept a package that cost more than $350 billion.

Grassley then reportedly called Vice President Cheney to come mediate the dispute, which was ongoing as Roll Call went to press on Wednesday. The flareup threatened to prevent both men from making good on their promise earlier in the week to have a harmonious bill on the president’s desk before Memorial Day.

Indeed, the involvement of the leadership of both chambers is often called upon to help settle disputes between the two chairmen, who regularly jockey for the right to chair conference committees and are rumored to have resorted to a variety of ploys to prevent the other from presiding over high-profile House-Senate negotiations.

Both are experts in the vagaries of tax and health care policy. In fact, much of the White House and Congressional GOP agenda must wend its way through their panels. That includes this year’s tax cut, a prescription drug benefit under Medicare and an overhaul of Medicaid.

But their ability to work together has often been complicated by their differing approaches to wielding power.

“It forces negotiations through another layer. … through third-party intervention,” said a senior Senate GOP aide, who noted Speaker Dennis Hastert (R-Ill.) was often called to moderate for Thomas.

Indeed, Grassley often irks Thomas with his strong desire to work with Democrats even if their votes aren’t needed for Senate passage.

“That’s the nature of their chamber,” said one GOP House Member. “To frustrate the hell out of us.”

Meanwhile, Thomas’ hard-charging, take-no-prisoners style gets under Grassley’s skin.

“Grassley is such a nice and decent man, and Thomas just doesn’t take him seriously,” said one senior Democratic Senate aide.

Republicans agreed that Thomas’ approach can sometimes overwhelm Grassley.

“Bill Thomas can be very aggressive in conference. … Sometimes it’s too much for laid-back Senator Grassley,” said one senior Senate GOP aide. “Bill Thomas has a way about him that is very much a lone ranger. For example, on the dividend proposal, he took a different approach from the White House. He’s not listening to what the White House is saying.”

In the end, it was that different dividend approach — lowering the tax rate on dividends to 15 percent, rather than the White House’s original desire to eliminate taxes on dividends — that won the Bush administration’s favor this week as negotiations between Thomas and Grassley carried on late into the nights.

One Senate GOP aide said that White House decision “undercut” Grassley in the conference talks and caused a considerable amount of anger on the Senate side, where the White House had aggressively pushed Grassley and Budget Chairman Don Nickles (R-Okla.) to champion an all-out repeal of dividend taxes even if it was temporary.

Despite some criticism that he is not forceful enough, many in the Senate warned that Grassley’s abilities to win concessions from Thomas should not be underestimated.

“Don’t sell Grassley short. He gives you that podunk stuff, but he wasn’t born yesterday,” cautioned another Republican Senator.

Others said Grassley’s nature is more compromising, so it may appear that he’s losing ground even when he’s not.

“Senator Grassley’s approach to the issues is much more in tune with the [Senate GOP] leadership and the political center of the U.S. Senate,” said a senior GOP Senate aide.

While the two have to come together primarily during House-Senate conferences, their disagreements even extend to who gets to wield the gavel at such meetings and who will serve as co-chairman.

Though a bill to give active military personnel tax breaks appeared to be a slam dunk in both chambers, Republicans and Democrats alike were puzzled by Thomas’ decision to load the popular bill, designed to help troops fighting the war in Iraq, with a slew of tax breaks for makers of fishing tackle boxes and other unrelated interests.

Many theorized that the reason Thomas had loaded the “patriotic” tax bill with other provisions was to force a House-Senate conference. Indeed, Grassley declined to include Thomas’ add-ons in his version. Because Grassley was next in line to chair a conference committee, he would take charge of the military tax-break conference, while Thomas would then be in line to chair the conference on the president’s growth package.

As it stands now, the military tax bill, which unanimously passed the House after Thomas agreed to strip the extra provisions, still has not been sent to conference to work out what are now just minor differences between the two chambers’ versions, said aides.

Grassley did include the measure in the Senate’s version of the tax cut, which would make it conferenceable as part of the growth package, of which Grassley remains in line to chair.

But again, in what could be another effort to prevent Grassley from heading the conference, the House had not appointed conferees on the tax cut as of Wednesday, while the Senate appointed them on May 15. All the negotiations this week have gone on behind closed doors, without a designated chairman and without much Democratic participation.

One Senate GOP aide said Grassley and Thomas had actually reached a deal earlier that Grassley would chair the tax conference, while Thomas would get to chair any Medicare prescription drug conference. It was unclear this week whether that is still the deal, however. Typically, House and Senate chairmen alternate chairmanships of conferences.

Still, some Members and aides defended the relationship between the two chairmen.

“They have a good relationship, which one may be surprised about given their different personalities,” said Rep. Jim McCrery (R-La.), a Thomas ally on Ways and Means.

One Senate GOP aide noted that Grassley has essentially learned to work with Thomas by playing to Thomas’ desire to be right.

“Grassley’s approach to getting things done is making everyone feel like they’re winners, and not acting like he’s getting something over on people,” said the aide. “[Grassley’s] persistent, but he has a way of calming the situation.”

This aide noted that Thomas appears to want to produce a good product and that helps his relationship with Grassley.

“It’s not all negative as far as Thomas goes. I think he wants for both of them to come out winners, too, if possible. If it’s not possible, obviously, he’s going to look out for himself,” said the aide.

The aide continued, describing negotiations on Tuesday evening, “I don’t see the Grassley-Thomas relationship as confrontational or as negative as maybe people view it. For example, last night, there was never one point where either one of them blew up at the other. There were some serious moments, but no blowups.”