WASHINGTON -- As the White House and allied Democrats begin a high-stakes push to replace Justice Antonin Scalia on the Supreme Court, they are coping with a major hurdle: they have little to no leverage over Republicans.

The process for replacing a justice on the court is supposed to be simple. The Constitution gives the president the authority to make a nomination, and gives the Senate the power to advise and consent. When there have been vacancies in the past, things have proceeded in a straightforward way. A name is offered up and the Senate Judiciary Committee receives it, holds hearings and votes on it. Presuming the nomination passes through the committee, it goes to the full chamber. Though the nominee could be subjected to a filibuster, in which 60 votes are required for confirmation, that's really only happened once, and whether it was technically a filibuster remains in dispute.

But we live in illogical times. In the immediate aftermath of Scalia's death on Saturday, Senate Republicans said that not only are they likely to filibuster President Barack Obama's eventual nominee, but they would not even bother holding a hearing, in hopes of delaying the matter until a Republican is in the White House. And Senate Democrats, who are in the minority, are largely powerless to change this dynamic.

"No we don't," said Anita Dunn, a long-time party operative, when asked if Democratic leadership had much leverage in the upcoming fight.

Jim Manley, a former top aide to Senate Minority Leader Harry Reid (D-Nev.), said it was unlikely for a nominee to move forward. "Is there any leverage, no," he said.

Even those occupying positions of power concede that the procedural cupboard is bare.

"I don't know of any that are allowed," Sen. Chuck Schumer (D-N.Y.) said, when asked if there were mechanisms that might allow the party to put Republicans on record.

Olivier Douliery via Getty Images Sen. Chuck Schumer (D-N.Y.) thinks Democrats will have trouble getting a nominee confirmed to the Supreme Court.

So party officials are turning to a shaming campaign, seeking to badger Senate Republicans and label them obstructionists, in hopes that a few of them -- presumably those with uphill re-election battles -- will stop echoing the party line. Obama, speaking at a press conference on Tuesday, made the argument that refusing to consider a nominee would show clear disregard for constitutional norms.

"I’m amused when I hear people who claim to be strict interpreters of the Constitution suddenly reading into it provisions that are not there," he said. "This will be another test whether norms, rules, basic fair play, can function in Washington these days."

But other Democrats have made more overt threats should Republicans demand that a replacement for Scalia only be considered by the next president.

"I think this could be a high-water mark where Republicans just reach so far that they get punished in the elections, and realize that if they don't get back to reality and let us vote they could be punished severely," said Schumer.

Recognizing the competing pressures Senate Majority Leader Mitch McConnell (R-Ky.) will face, Schumer predicted that he would eventually conclude that control of the Senate was more important than the affection of his base. "You know, survival is very important both for McConnell and the Republicans who are up for re-election, and I think they are going to really suffer here," he said.

Already, there is some evidence of Republican anxiety. Sen. Thom Tillis (R-N.C.) has encouraged his party to at least hold hearings on a nominee. Sen. Susan Collins (R-Maine), in a 57-word statement that said barely anything, suggested her party shouldn't rush to judgment. And Sen. Ron Johnson (R-Wis.), up for re-election this year, backtracked on Tuesday to say he'd be open to hearings. Sen. Chuck Grassley (R-Iowa), who chairs the Judiciary Committee, left the door ajar to holding hearings. And outside Congress, several operatives and legal officials have said that the process of replacing a justice is too sacrosanct to succumb to partisan gridlock.

ASSOCIATED PRESS As chair of the Senate Judiciary Committee, Sen. Chuck Grassley (R-Iowa) has a big say in whether a Supreme Court nominee will get a hearing.

White House officials have gleefully pointed to these developments as evidence that the dam is cracking. But even they aren't confident that it will fully break.

After all, as an addendum to his call for hearings, Tillis encouraged Obama to nominate someone who echoed Scalia's ideology and jurisprudence, which would make sense if Obama were a conservative. Alas, he's not. And while Johnson said he'd be open to hearings, he didn't bother to feign openness to the possibility that he would vote yes. "I don’t think there’s much of a difference one way or another," he said.

"If you take McConnell at face value, I can't imagine he will reverse course," said Manley. "There will be hell to pay within his caucus and among Republican activists if he decides to do so."

Faced with this, sources close to the administration say that Obama is leaning toward nominating someone who has been confirmed by the Senate before, who has either an apolitical resume or good existing relations with current senators. That type of nominee, they hope, would be difficult for Republicans on the Judiciary Committee to reject outright, especially given the fact that the voting public can't fathom what the fuss is all about. They point to past standoffs over funding for the Department of Homeland Security and Planned Parenthood, as well as raising the debt limit -- instances in which Republicans initially demanded strict policy concessions only to eventually fold -- as precedent.

"I just don't think the politics of obstruction play well -- especially when Republicans are facing a tough map, in a presidential election year ... AND obstruction vis a vis the court, which is supposed to be an apolitical body," emailed Ben LaBolt, a former Obama administration spokesman on judicial matters.

But at some point, the shaming campaign will have diminishing returns. Were a nominee to actually get a hearing, Democrats would still need to get him or her through the committee. Then, they'd need McConnell to bring the nomination up for a vote and, potentially, five Republicans to vote for full passage. And even at this juncture, top officials aren't willing to demand that last step.

"Members are going to continue to vote 'no' as I have done," said Schumer, noting that in 2007 he called for lawmakers to consider but not support President George W. Bush's nominees for the court till he left office. "But that doesn't mean there should be no consideration."

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