Senate Majority Leader Harry Reid (D-Nev.) on Tuesday threw his weight behind a plan to have superdelegates in the Democratic presidential primary make their votes public by July 1.

“I like that — July 1 or before,” Reid said of a plan floated last week by Democratic National Committee Chairman Howard Dean for superdelegates to show their hands between the end of primary season on June 3 and July 1.

Asked what he was going to do to encourage such a plan, Reid told Roll Call, “I just did it.”

Roughly 40 percent of superdelegates, the unpledged appointees to the national convention in August who are likely to decide the contest, are Members of Congress. Their support is almost evenly split between the two Democrats pursuing the party’s presidential nod, Sens. Hillary Rodham Clinton (N.Y.) and Barack Obama (Ill.). Of the 285 Members of Congress who are superdelegates, 94 are backing Clinton, 87 are supporting Obama and 104 are publicly undecided.

But Democratic leaders are worried that the increasingly negative tenor of the contest could hurt their chances in November against presumptive GOP nominee Sen. John McCain (Ariz.). With that in mind, party elders have been vetting ideas for how to end the contest smoothly, with Dean’s idea the latest to take hold.

Reid and Speaker Nancy Pelosi (D-Calif.) have remained steadfastly neutral in the Clinton-Obama race.

For her part, Pelosi made more noncommittal comments Tuesday, suggesting that she hoped the contest would be resolved by the time the primaries conclude. Asked whether she would support setting a cutoff date if the race does not end by then, she said, “No, I think it will work its course” on its own.

Parsing her words carefully on the subject, Pelosi explained that superdelegates should pick a candidate based on their conscience and by “paying attention to the will of the people.”

She said the issue “needs to be resolved sooner than later” to ensure that there is a unified Democratic Party heading into the November elections. “We don’t want to diminish any enthusiasm” among Democratic volunteers and fundraisers, Pelosi said.

Meanwhile, across the Capitol, Sen. Patrick Leahy (D-Vt.), an Obama backer, said his earlier comments asking Clinton to get out of the race were “blown out of proportion” by Clinton’s Vermont campaign chairman.

Leahy said that at some point, Democrats need to field a single candidate to take on McCain. He said he simply wants to see an end to the protracted Democratic fight, which is hampering the party’s ability to look ahead to November.

“The main reason I spoke out is because I’d like to see us start running against the Republican nominee and not against each other,” Leahy said, adding that both Clinton and Obama are “eminently well qualified” to be president.

Leahy has plenty of support on that point, but none of his fellow Democratic Senators appear willing to join him in calling for Clinton to leave the race. Many Democrats said they hope the nomination is worked out before August and are in favor of setting a date for uncommitted superdelegates to declare their preferences.

“I think it makes sense,” said Sen. Benjamin Cardin (Md.), one of the uncommitted Democrats. “We should try to complete the process before” the convention.

Sen. Ben Nelson (D-Neb.), an Obama supporter, said Dean’s proposal is “one way to deal with the issue,” but there are other proposals also worth considering. Nelson is floating a plan that calls for superdelegates to withdraw from the process altogether and allowing the winner of the pledged delegates at the conclusion of the primaries to claim the nomination.

“I hope the two candidates can work it out. That’s my preference,” Nelson said. “But we have people — such as myself — who have some ideas. I think we should pick from the best of the suggestions and find a resolution.”

Other Senators said they want the primaries to continue before attempting to intervene. Sen. Sheldon Whitehouse (D-R.I.), a Clinton supporter, said that if individuals like Dean want to “encourage people to make decisions sooner, it’s certainly his prerogative.” But Whitehouse said he was opposed to any attempt by party elders to enforce a deadline on superdelegates.

Asked his thoughts about whether Clinton should abandon her bid, Whitehouse said: “It’s far from clear that Sen. Clinton wouldn’t be our strongest general election candidate. … I think it would be a mistake for her to get out of the race.”