After laying low for the early portion of the primary campaign, a growing number of Democratic Senators are considering endorsing one of the remaining contenders for the nomination.

With the race thrown wide open by Monday’s Iowa caucuses, Senate Democrats said they are coming under increasing pressure to endorse — particularly those Members whose states are voting on Feb. 3 or soon thereafter.

The crown jewel of endorsements, in terms of the seven states up for grabs Feb. 3, would be Sen. Fritz Hollings (S.C.). The retiring Senator had previously said that he would remain neutral in his state’s primary, which will be the first Southern contest and the first with a large percentage of black voters.

Hollings said Tuesday he is now very much considering an endorsement but has yet to make up his mind. “I keep thinking about it, and that’s what I’m doing right now,” he said. “I’m looking at it.”

Senators were careful not to put too much stock in the power of their endorsements, especially considering how the backing from one of their colleagues, Sen. Tom Harkin, provided little benefit to former Vermont Gov. Howard Dean in Iowa.

But voters in the states up for grabs in February have seen nowhere near as much of the candidates as those in Iowa or New Hampshire, where the first primary is set for Tuesday, and the late backing of a prominent statewide elected officer may help tip the scales a few points toward one of the candidates.

In addition to Hollings, Sens. Kent Conrad (N.D.), Carl Levin (Mich.), Debbie Stabenow (Mich.), Maria Cantwell (Wash.) and Charles Schumer (N.Y.) all suggested Tuesday they could soon make endorsements.

No Senator would give any indication of which candidate he or she would back, but several indicated they are approaching the decision in the most pragmatic of ways, trying to find the challenger who best matches up against President Bush.

Asked if he had any criteria for endorsing, Hollings responded, “Yeah, who can beat Bush?”

As the primary challengers have looked at the schedule and the map, they aren’t necessarily looking strictly at big states, either, in endorsements. They’re looking for someone who can deliver a win, according to the Senators being courted.

Sen. Joseph Biden (D-Del.), who has stated he’ll not endorse in the Feb. 3 Delaware primary, said he took phone calls Friday regarding his endorsement from Sen. John Kerry (Mass.) and Rep. Richard Gephardt (D-Mo.), who dropped out of the race Tuesday after finishing fourth in Iowa. He received messages the day before from Dean and retired Gen. Wesley Clark.

Even with Kerry on the rise after his Iowa win and Gephardt out, Biden said he still has no plans to endorse, something each candidate was happy to hear once he realized Biden wouldn’t endorse him.

Another small state up for grabs Feb. 3 is North Dakota, where most of the candidates have campaigned but no one has spent a large amount of time or resources, making Conrad’s flirtation with the candidates a potentially big prize.

“Several of the candidates called this weekend,” Conrad said. “I’m talking to all of the campaigns.”

The pressure is only mounting on those Senators openly considering an endorsement. “I’ve gotten a lot of calls from a lot of people, including the candidates themselves,” Levin said.

Stabenow echoed that sentiment: “I’ve heard from everybody. I’ve gotten calls today.”

To this point in the campaign, only 10 of the 49 members of the Senate Democratic Caucus have endorsed a presidential candidate. And only four of those endorsements came from Senators who are backing someone other than a home-state colleague. By contrast, 125 out of the 205 members of the House Democratic Caucus had endorsed a candidate by Friday.

Hollings admitted that his long-standing pledge to remain neutral was mostly done as a way to make sure that the Palmetto State’s primary would be seen as a wide-open race and that the party leaders wouldn’t pick sides, drawing as many candidates as possible into the mix. “It’s worked: They’re all coming,” Hollings said.

Some Senators in the upcoming primaries are taking divergent paths from their home-state colleagues. While Conrad seems likely to endorse in the North Dakota battle, Sen. Byron Dorgan (D-N.D.) repeated his contention Tuesday that he would remain neutral. “I’m just going to let them go at it,” Dorgan said.

Sen. Patty Murray (D-Wash.) said she has no plans to endorse in her state’s Feb. 7 caucus, but Cantwell is open to the idea. “I’m digesting it,” Cantwell said.

For candidates running for re-election this year, endorsing someone might be a bit dangerous if the Senator backs the wrong candidate, potentially angering the eventual nominee. Dorgan and Murray are up for re-election in November, as is Sen. Barbara Boxer (Calif.), who said Kerry and Sens. John Edwards (N.C.) and Joe Lieberman (Conn.) are “like brothers to me.”

Unlike Sen. Dianne Feinstein (Calif.), who was an early backer of Kerry, Boxer plans to remain neutral even if the campaign is still in flux by the time of the March 2 primary in the Golden State. “I’m so focused on my own race right now,” she said. “I foresee myself focusing on post-March 2.”

If the race is still in play March 2, when California and other big states such as New York are up in the primary calendar, Schumer’s backing may be the biggest reward in the Empire State. “I’m thinking about it, that’s about it,” he said of an endorsement.

That puts him in the opposite corner of Sen. Hillary Rodham Clinton (D-N.Y.), who reiterated her pledge Tuesday to remain neutral in the primary. “Nothing has changed,” she said.