Sen. Hillary Clinton (D-N.Y.)

Rep. Jason Altmire (D-Pa.) said he was encouraged on Monday to back Obama now, and while the uncommitted freshman member will not support a candidate until later this week, he expects other lawmakers to endorse on Tuesday.

One such member is House Majority Whip James Clyburn (D-S.C.), who said he will announce his endorsement at 11 a.m. Tuesday. Clyburn told the AP that he will endorse Obama.

In an interview with The Hill, Altmire said the Obama campaign believes it can reach the 2,118 delegates needed to clinch the nomination on Tuesday. The plan would be for superdelegates to formally endorse Obama while the polls are still open, and then later Tuesday, Obama would gather enough delegates to reach the magic number.

That strategy would ensure that voters and pledged delegates — and not an individual superdelegate — would put Obama over the top, helping to avoid the perception that party insiders ultimately decided the nominee.

There are 72 Democrats on Capitol Hill who have yet to endorse a candidate and roughly 200 uncommitted Democratic superdelegates in total.

Altmire said he personally promised Sen. Hillary Rodham Clinton (D-N.Y.) that he would not make an endorsement until after June 3 and will honor that commitment.

Clinton’s campaign has said it believes it can change the minds of superdelegates, but Altmire said he “can’t envision anyone” who would switch from Obama to Clinton at this point of the race.

Altmire said he has been in contact with other uncommitted superdelegates.

Sen. Tom Harkin (D-Iowa), meanwhile, called a few of the Senate’s remaining uncommitted superdelegates for a Monday afternoon meeting to discuss how each plan to roll out their endorsements in the coming days. The Obama and Clinton campaigns were not represented at Monday’s meeting, which took place outside of the Capitol.  Other than Harkin, Sens. Ben Cardin (D-Md.), Tom Carper (D-Del.) and Ken Salazar (D-Colo.) attended the meeting.

The Obama campaign did not respond to a request for comment.

In recent weeks, roughly three of every four Democrats on Capitol Hill have endorsed Obama. This endorsement trend comes as Clinton has won recent contests and made her case that she is more electable than the Illinois senator.

Asked last week whether there is any chance they will endorse soon, a handful of members suggested that a formal announcement is in the works.

Sue Walitsky, spokeswoman for Cardin, said the senator “is waiting for all the primaries to finish before he makes his decision.”