"I don't envy him the decision, but I think he's going to make it soon," Judiciary Committee Chairman Patrick Leahy, D-Vt., told The Associated Press after a private White House session. "I think when he goes out west today and tomorrow, he's going to have a lot of stuff on the airplane with him."
Obama was leaving later in the day to give a commencement speech at Arizona State University, while the debate simmers about the nomination of a successor to retiring Justice David Souter.
Asked if the president ran some names of candidates by the senators, Minority Leader Mitch McConnell said: "No. No names."
Obama's bipartisan consultation comes as he zeros in on a nominee. Souter is part of the court's liberal wing, and his replacement by the new Democratic president is not expected to change the high court's ideological balance. Obama is widely expected to appoint a woman to replace Souter, and is under pressure from some Latino officials to name the nation's first Hispanic justice.
Obama met with Senate Majority Leader Harry Reid, D-Nev.; Sen. Jeff Sessions of Alabama, the top Republican on Judiciary; Leahy and McConnell. Vice President Joe Biden, a former Judiciary Committee chairman and veteran of confirmation hearings, attended, too.
Sessions said that Obama didn't give a timeframe for his decision but indicated he wanted to get it done soon. "My impression was he doesn't want to let it take too long," Sessions told reporters on the White House driveway.
The White House has said Obama will not announce a decision this week. It appears increasingly likely, though that he will do so before month's end.
One official said none of the senators present at the closed-door White House meeting mentioned the names of any potential nominees.
"The president said we may disagree on how to vote on a nominee, but we can agree on the process, or the tone of it," Sessions said. "I think that's true."
Obama wants his nominee confirmed before the Senate goes on recess for the summer in early August. But the senators would not commit to that.
Reid said the chamber would not be wedded to "arbitrary deadlines" and cautioned about the Judiciary Committee's busy schedule.
"We'll work out a decent schedule," said Leahy, who promised a fair chance for Republicans and Democrats to ask questions during confirmation hearings. "Let's get the nominee first."
An emerging point of debate is Obama's insistence that his nominee be someone who is willing to show "empathy" in making rulings. Some Republicans have balked at the notion, including Sessions, who wrote an op-ed on Wednesday prodding Obama not to pick someone who would rule based on personal feelings.
Asked whether that matter came up, McConnell said: "We did have a discussion about the importance of following the law, and not acting like a legislator on the bench."
Should Obama make his pick shortly, that would leave June and July for his nominee to potentially get through vetting process, and voting presumably would happen in the Senate by August. It is possible, though, that the confirmation process would carry on into September.
Leahy said he saw no problem in having a nominee confirmed by the start of the new court session in October.
Obama's thinking is largely driven by his own life: community organizer in Chicago, president of the Harvard Law Review, instructor of constitutional law, member of the Senate during two Supreme Court confirmations. He is not just setting the tone; he is engaged in the search.
What's known is that Obama is likely to choose a female candidate for a nine-member court that has just one woman, Ruth Bader Ginsburg. He is expected to choose a relatively young person who could serve for decades and may opt for someone from outside the traditional path of the federal appellate system.
Outside groups and even the Senate's newest Democrat, Arlen Specter of Pennsylvania, have urged Obama to choose a female, arguing that women are underrepresented on the court. Other organizations have pressed for the president to select a Hispanic.
The White House, determined to cast Obama's decision as his own, has signaled to advocacy groups to keep their campaigns to themselves. Still, some of those groups will get an audience of their own Wednesday at the White House with senior staff to make their cases.
"I don't think that the lobbying of interest groups will help," said press secretary Robert Gibbs. "I think in many ways lobbying can, and will, be counterproductive."
Obama may be in position to make at least one more nomination this term due to retirement. Ginsburg is 76 and recently underwent cancer surgery. Justice John Paul Stevens, 89, is the oldest member of the court.