The 34 House Members who had backed Democratic Rep. Richard Gephardt’s (Mo.) presidential bid weren’t rushing Tuesday to endorse any of his rivals, despite immediate lobbying efforts by the competing campaigns.

The 27-year House veteran abandoned his White House bid Tuesday afternoon after a lackluster fourth-place showing in the Iowa caucuses — a contest seen as a must-win for the former House Democratic leader from Missouri. While the move frees his backers to jump aboard one of the seven remaining Democratic campaigns, Gephardt’s Congressional supporters said they would take a cautious approach regarding whether and whom to endorse next.

House Democratic aides and Members insisted it will be at least a week — perhaps longer — before Gephardt’s one-time backers start endorsing again.

“There are maybe some who had been torn between Gephardt and another specific candidate and could do something this week,” said one senior House Democratic aide. “But I think the majority will wait until New Hampshire.”

Next Tuesday’s New Hampshire primary could show whether Sen. John Kerry (Mass.), who took first place in Iowa, can solidify his new frontrunner status and whether former Vermont Gov. Howard Dean’s campaign still has legs. It also could make or break Connecticut Sen. Joe Lieberman and reinforce the insurgence of North Carolina Sen. John Edwards and the strength of retired Gen. Wesley Clark.

Even with 34 backers and still other loyalists in the House, Gephardt failed to ignite a firestorm of support among his colleagues. He even had captured the endorsements of many prominent Members, including four of the top five House Democrats: Minority Leader Nancy Pelosi (Calif.), Minority Whip Steny Hoyer (Md.), Democratic Congressional Campaign Committee Chairman Robert Matsui (Calif.) and Caucus Vice Chairman James Clyburn (S.C.).

Caucus Chairman Bob Menendez (N.J.), the No. 3 Democrat, has endorsed Dean.

But before Gephardt even announced his formal withdrawal, the competing presidential campaigns were calling prominent House Democrats to solicit support. Clark, Edwards, Kerry and the Rev. Al Sharpton were among those reaching out to Gephardt’s backers, sources throughout the Caucus said.

Pressure aside, several well-placed House Democratic aides said they wouldn’t be surprised if the party leadership in particular remains uncommitted until a nominee has been crowned. Jumping on two unsuccessful campaigns may not be the smartest political move for Members, they said.

Pelosi, courted Tuesday by both Clark and Edwards, said she did not plan to endorse a Gephardt competitor but would support the ultimate Democratic nominee.

“People are trying to be careful,” said one House Democratic aide.

“Given the volatility [in the race], a lot of people are remaining neutral,” said Matsui, explaining that many of the lawmakers who endorsed Gephardt did so not for strategic reasons but because of their long-standing relationships with him. “In my situation, particularly with the DCCC, it’s probably best if I don’t endorse anyone.”

But some of Gephardt’s one-time backers said they are impressed with several of the other camps, mentioning those of Clark, Edwards and Kerry. Edwards, who had kind words for Gephardt following the Iowa result, is rumored to be attracting some of Gephardt’s campaign staff and could also win favor with some of his Congressional supporters.

Edwards is leaning hard to capture Clyburn’s second endorsement in advance of the Feb. 3 South Carolina primary, House Democratic sources said. As a prominent lawmaker from a key Southern state with a large black population, the African-American Congressman’s backing is viewed as particularly significant for Edwards’ campaign.

Asked Tuesday whether he still viewed himself as a potential kingmaker for the Democratic nomination, Clyburn responded: “No. I never did.”

The prominent South Carolina lawmaker also insisted Tuesday that he’s in no hurry to board another campaign and wouldn’t even say whether he would endorse before his home state’s primary. He said he’s “going to chill out for a while” but acknowledged many of the campaigns have reached out to him since Iowa and “asked for my help.”

“I have an emotional attachment to Dick Gephardt and his family,” Clyburn said. “I will talk with them before I make any decisions.”

Hoyer, who said he’d been called by Clark early Tuesday, said he was holding off on tossing his support behind anyone new, calling Gephardt a friend. He said while he “may” endorse another candidate before the party nominee is clear, he added: “I have no intentions right now.

“No one is waiting in New Hampshire for what Steny Hoyer has to say,” Hoyer quipped.

Hoyer will sit down next week with fellow Gephardt backers and Maryland Democratic Reps. Benjamin Cardin and Dutch Ruppersberger to talk about whether and whom to endorse now. Maryland’s primary is in March, giving those candidates some time to decide, Cardin and Ruppersberger said separately.

“What I’m working on is who is in the best position to beat [President] Bush,” Ruppersberger said.

Rep. William Lacy Clay, Gephardt’s national co-chairman who campaigned extensively for his fellow Missourian, said he too is taking a wait-and-see approach to his endorsement.

“I’m going to relax for a while and sit back and assess” the landscape, he said. “It’s too early.”

Ben Pershing contributed to this report.