(CNN) Senior Senate Republicans are growing more comfortable with the idea of denying President Barack Obama's Supreme Court pick a hearing, arguing privately that the risk of giving the nominee a platform to shine far outweighs the benefits.

The party's strategy isn't yet fully formed and won't be until GOP senators return to Washington next week. But in back-channel conversations with senators and among senior party officials, Republicans are arguing that denying a hearing to Obama's choice would allow them to better make the case that voters should have a say in the next Supreme Court justice -- not members of the Senate and a lame-duck president.

If Republicans held confirmation proceedings, several Republicans told CNN, that argument would be badly muddied. Moreover, they risk giving Obama's choice an opportunity to detail his or her life story and legal qualifications, and they'd rather stop the nominee before giving the White House and Senate Democrats a chance to build momentum.

"There's little upside to it," said one senior GOP source who asked for anonymity to discuss party strategy.

And for vulnerable GOP senators, several Republicans argued that it would be much better politically for those members to avoid a vote, rather than have to cast a judgment on the merits of nominee who could be well-qualified and well-liked.

Senate Majority Leader Mitch McConnell has been intentionally vague about his plans, rushing out a statement Saturday evening to ensure he got ahead of his party's presidential candidates who were debating that night in South Carolina. In his statement, McConnell said that the vacancy "should not be filled until we have a new president," adding that the American people "should have a voice." But he did not explicitly weigh in on the idea of holding hearings or a floor vote.

On Wednesday, McConnell sent an email to GOP donors on behalf of the National Republican Senatorial Committee touting his hard line.

"Senate Republicans have made a commitment to ensuring that the American people have a voice in the selection of the next Supreme Court Justice," McConnell wrote. "I hope you will join us by signing the petition to stand with Senate Republicans as we hold our ground in waiting to confirm a new justice until after 2016, the time by which the American people will have chosen a new president and a new direction for our country."

McConnell plans to consult with GOP senators in detail next week, when his 54-member conference will begin to lay out their various options and meet for the first time since Antonin Scalia's death created a vacancy on the court. If there's a groundswell of GOP support for a public hearing, particularly among Republicans endangered in the November elections, McConnell could green-light Senate Judiciary Chairman Chuck Grassley to move forward with hearings.

But no Senate Republicans have yet demanded public hearings, a sign that the idea of not taking up the nomination is still the most popular one.

"I think Mitch McConnell was correct," Sen. Johnny Isakson, a Georgia Republican up for reelection this year, said in an interview Wednesday. "It's not a matter of not going through a confirmation process, it's a matter of which confirmation process you go through -- one now that's a rush or one next year after the next president of the United States comes to office. I prefer the latter."

Tactical debate

Republicans almost universally say that Obama's nominee will be blocked, but the debate is squarely over how and when.

The two leading options come down to this: Tell the public that the nominee will be given a fair hearing, go through the public vetting process and ultimately whip their members to kill the nomination either on the floor or in the Senate Judiciary Committee. Republicans could afford no more than one defection in committee. If the nomination advanced, Democrats would need to muster 14 GOP votes on the floor to break a likely filibuster attempt.

On Wednesday, Republicans privately said that going through that process would be highly unpredictable -- and give Democrats a chance to turn the debate in their favor. But publicly, the GOP continued to be coy about their intentions.

"It's entirely up to the chairman of the Judiciary Committee whether even to schedule a hearing on the president's nominee," Texas Sen. John Cornyn, the No. 2 Senate Republican and senior member of the Judiciary panel, told a Dallas radio station. "And were the nomination to get out of the Judiciary Committee, it's entirely within the control and discretion of the Senate majority leader, Sen. Mitch McConnell, whether to schedule it for a vote, which does demonstrate that majorities do matter. ... I happen to believe we ought to leave this appointment to the next president.

Other Senate Republicans have signaled that they wouldn't be opposed to Judiciary Committee hearings, including Sen. Ron Johnson of Wisconsin, who told a local radio station he's "open" to the idea but he said he sided with McConnell's call to punt the issue until after the elections.

Other Republicans are lining up behind the call to punt the matter as well. Speaking to CNN's Wolf Blitzer Wednesday, Utah Sen. Orrin Hatch, the most senior Republican in the Senate and member of the Judiciary Committee, said that there was no need to hold hearings this year.

"All it would take is for Sen. Grassley to just say, 'Look, we're not going to confirm anybody this year,' Hatch said.

Democrats seize a political opening

Democrats plainly believe that Republicans will suffer badly if they are perceived to be obstructing a well-qualified nominee from advancing, particularly senators from swing states.

Rep. Ann Kirkpatrick, an Arizona Democrat challenging Sen. John McCain, said his position to wait until after the election is "a complete contradiction of where he's always been."

Kirkpatrick added: "Now that it's an election year, he's saying something completely different."

McCain spokeswoman Lorna Romero said Kirkpatrick is a "rubber stamp" for the Obama agenda, while adding that "this is obviously not your average judicial nomination" given that it could tip the ideological balance of the court over the next several decades.

On Wednesday, Sen. Chuck Schumer of New York, who is expected to be the next Senate Democratic leader, led a press conference call with several progressive interest groups that announced they have collected 500,000 signatures on a petition demanding the GOP allow a vote on a nominee.

"Grass-roots voices are going to be the key to getting Sen. McConnell to back off and let the Senate do its job," said Schumer. "The level of obstruction we've seen since Saturday is mind-boggling. It's unprecedented, it's wrong, it's unsustainable and it is against our constitution."

Schumer seized on Grassley's comments as well as recent comments by Johnson and North Carolina Sen. Thom Thillis -- who both suggested they might be open to Senate consideration of a nominee -- as evidence Republicans won't be able to sustain their position.

"We're seeing that coalition begin to crack," Schumer said. "I believe that we will be able to have hearings and get a vote."