By the time Congress finishes a supplemental spending plan for the Iraq War, senior Democrats say, it is likely that voters in Iowa, New Hampshire, Nevada and South Carolina will have made their choice on White House hopefuls.

The “Super Tuesday” primaries probably will be over, too.

That political calendar — combined with the reality of how hard it is for Democrats to get left and center to agree — has caused some senior lawmakers to conclude that Congress will soon end up letting the parties’ presidential candidates take the lead on Iraq policy.

“The outcome of the presidential primaries will help to bring focus to the debate on Iraq in Congress,” said Rep. John P. Murtha, D-Pa., chairman of the Defense Appropriations Subcommittee.

House Majority Leader Steny H. Hoyer, D-Md., agreed, saying, “There’s no question that the presumptive presidential nominee will carry a lot of influence on the Iraq debate.”

Murtha, a close adviser to Speaker Nancy Pelosi, D-Calif., said he has advised the leadership to put off the supplemental spending debate until early 2008 to allow time for Democrats to form more consensus on Iraq.

The supplemental will be the vehicle for the big showdown on whether to continue funding for the war, and “it will be decided in January or early February,” he said.

Congress has a target adjournment of Nov. 16, and there won’t be any urgency to make a decision before January, Murtha argued. “There is enough money in the pipeline until then,” he said.

The leadership is not willing at this stage to be pinned down on a timetable for the supplemental. “We will be discussing it over the next few weeks,” Hoyer said. There are a lot of factors. I don’t want to pinpoint any one factor.”

But senior appropriators James P. Moran, D-Va., and David E. Price, D-N.C., said Murtha’s opinion would carry considerable weight. “The short answer is we will probably follow Mr. Murtha’s advice,” said John B. Larson of Connecticut, vice chairman of the House Democratic Caucus.

Hoyer and Majority Whip James E. Clyburn, D-S.C., confirmed that the supplemental had no place on the immediate floor calender and said it was unclear when it would go to the floor.

But the push to delay action on funding has run into flak from liberal Democrats, who fear they are losing votes for their position.

“I would like to see the showdown now, rather than waiting until next year,’’ said Judiciary Chairman John Conyers Jr., D-Mich.

Some Republicans also criticized the notion.

“I’d like to see the Democrats move the supplemental as soon as possible. They should not be playing politics with this,’’ said Eric Cantor, R-Va., the chief deputy whip.

“I think it’s inane for us to wait,” said Jerry Lewis of California, ranking Republican on Appropriations.

But Deborah Pryce, R-Ohio, a moderate who is not running again, predicted that many Republicans would welcome putting off further showdowns on Iraq until the winners for each party emerge from the primaries.

“Each party will be looking for its presumptive leader to begin to lead at that point,” she said. “The Democrats almost already have that in Hillary [Clinton]. I hope that the candidates for both parties will help to move us to the center.”

Former House Speaker J. Dennis Hastert, R-Ill., also predicted a softening of the debate’s ideological edges.

“By early next year, there will be a coming together [for] both parties and their presidential candidates. And they will be moving to the center on Iraq and other issues. By March, it will all be about presidential politics,” he said.

Minority Whip Roy Blunt, R-Mo., said Republicans would closely watch where the front-runners for the two parties line up on Iraq after Super Tuesday, on Feb. 5.

“A lot will depend on the situation [in Iraq] at the time. And a lot will depend on what the presidential candidates are saying about Iraq after Feb. 5,” Blunt said.

Clinton, New York’s junior senator and the front-runner so far for the Democratic presidential nomination, said on “Meet the Press” on Sept. 23 that she would vote against the next supplemental “because I think that it’s the only way that we can demonstrate clearly that we have to change direction.”

But she has also distanced herself from proposals that would rapidly reduce troop levels and end the war next year.

At the Democratic presidential debate in Hanover, N.H., on Sept. 26, she said it would be “my goal to have all troops out by the end of my first term.”

But she and the two other Democratic front-runners, Sen. Barack Obama of Illinois and former Sen. John Edwards of North Carolina (1999-2005), declined to promise that all troops would be withdrawn from Iraq by the end of their first term.

The leading GOP presidential candidates — former New York Mayor Rudolph Giuliani, former Sen. Fred Thompson (1994-2003) of Tennessee, Sen. John McCain, R-Ariz., and former Massachusetts Gov. Mitt Romney — have allowed little daylight between themselves and Bush on the war. Only Rep. Ron Paul, R-Texas, who trails in polls, has taken a strong anti-war stand with his proposal (HR 2605) to end the authorization for the war (PL 107-243).

Senate Majority Leader Harry Reid, D-Nev., said he believed that the Democratic presidential candidates in the Senate — who also include Joseph R. Biden Jr. of Delaware and Christopher J. Dodd of Connecticut — were already having a big impact on the Iraq debate by promoting their own initiatives.

Reid said he had made no decision on when the supplemental would move but added that the emergence of a presumptive Democratic nominee would help build consensus on Iraq.

Plus, he said, “It will take a lot of attention off of me, which will be nice.”