Senate Judiciary Committee Chairman Charles Grassley (R-Iowa). (J. Scott Applewhite/AP)

Senate Republicans clashed Wednesday over how to battle President Obama’s expected Supreme Court nomination as the White House left open the remote possibility that the president might sidestep a confirmation fight by making a rare recess appointment.

Obama has the option, while the Senate is in recess, of naming a replacement for Justice Antonin Scalia, who died Saturday. A recess appointee would serve until the end of the next session of Congress at the end of 2017.

White House officials did not dismiss the idea that the president could use the recess maneuver if the Senate fails to hold hearings and a vote on the nomination Obama has promised to send to the Senate.

“Our intent is to nominate an indisputably qualified individual to fill a vacancy on the Supreme Court,” White House press secretary Josh Earnest said Wednesday. “And our expectation is that the United States Senate will fulfill their constitutional responsibility to give that individual a fair hearing in a timely up-or-down vote.”

But Obama’s opportunity to make a recess appointment will probably disappear after Monday, when the Senate returns from its weeklong recess. Republicans, who control the Senate, are likely to keep the Senate officially in session continuously for the rest of Obama’s term.

Still, the mere hint of a recess-appointment showdown highlighted the sharp divide between GOP senators who favor completely blocking any action on a potential nominee and those who have left open the possibility of at least holding hearings and perhaps even votes.

Senate Majority Leader Mitch McConnell (R-Ky.) declared in the hours after Scalia’s death that his seat “should not be filled until we have a new President.” But since his statement Saturday, his Republican colleagues have not agreed on where precisely they ought to make their stand: Should they refuse to take any action whatsoever, responding to the demands of the conservative base? Or should they at least schedule hearings and procedural votes in order to blunt political attacks from Democrats?

On Tuesday, Senate Judiciary Committee Chairman Charles E. Grassley (R-Iowa) declined to rule out hearings on a nominee; on Wednesday two senior GOP senators rebuffed suggestions that the Senate should evaluate the president’s promised nominee.

Sen. Orrin G. Hatch (R-Utah), a former chairman of the Judiciary Committee, and Sen. John Cornyn (R-Tex.), a panel member and the second-ranking GOP leader, said that while the final decision will be Grassley’s, they did not see much point in holding hearings.

“We have a coequal and independent right to handle this as we see fit, and we’re not required to rubber-stamp this for the president,” Cornyn said in an interview Wednesday morning on KSKY-AM in Dallas.

After host Mark Davis told Cornyn that “there can be no surrender on this,” the senator assured listeners of the conservative talk-radio station that Grassley would “stand firm” against consideration of an Obama nominee.

Washington Post reporter Juliet Eilperin explains the difficulties ahead facing both Republicans and Democrats as they battle to fill the vacant Supreme Court seat left by the sudden passing of Associate Justice Antonin Scalia. (Dalton Bennett/The Washington Post)

Grassley told Iowa radio reporters Tuesday he would “take it a step at a time” and “wait until the nominee is made before I would make any decision” on hearings. A junior Judiciary Committee member, Sen. Thom Tillis (R-N.C.), said Tuesday that Republicans would “fall into the trap of being obstructionist” if they reject any Obama nominee sight unseen.

Another junior GOP senator, Dean Heller (Nev.), suggested Wednesday that a blockade would be unwise. “The chances of approving a new nominee are slim,” he said, “but Nevadans should have a voice in the process.”

Grassley spokeswoman Beth Levine suggested Wednesday that the six-term veteran, who has participated in hearings for 13 previous Supreme Court nominees, would continue to weigh his colleagues’ counsel, saying it would be “odd” for Senate Republicans to “signal to the White House precisely what the conference is going to do until at least they’ve had a chance to discuss it in person.”

Hatch, who served as the Judiciary Committee’s chairman or its ranking Republican from 1993 through 2004 and continues to sit on the committee, said in an interview that he worries that a political spectacle amid a presidential race could be “demeaning” to the nominee, the Senate and the panel’s reputation for conducting fair and serious work.

One presidential candidate, Sen. Ted Cruz (R-Tex.), sits on the committee and would probably participate in a confirmation hearing.

“My own personal feeling is, and this would absolutely be up to Senator Grassley and Senator McConnell, is that it would be better to not even have hearings,” Hatch said. “We are in the midst of one of the most obnoxious, terrible presidential campaigns that I’ve ever seen. I don’t want to see the courts be smeared by being in the middle of the process.”

Senate Democrats kept up pressure on their GOP counterparts Wednesday. Sen. Charles E. Schumer (D-N.Y.), speaking on a conference call, promised a surge of grass-roots outrage if the blockade goes forward. “We’re already seeing the Republicans begin to crack,” he said.

McConnell’s silence has only added to the intrigue. Advisers on Wednesday continued to point to the Saturday statement, which other Republicans interpreted as a vow not to act in any way on the nominee but did not specifically spell out the leader’s view.

His only communication with fellow Republican lawmakers has been a couple of emails sent to senators, according to a senior GOP aide familiar with the brief missives.

In one note, McConnell made clear that he did not expect the president to try to resort to a recess appointment before the Senate comes back into session Monday, and the other included an attachment to a Wall Street Journal editorial critical of Schumer for a 2007 speech on Supreme Court nominations. Otherwise, the aide said, McConnell told his colleagues only that they would discuss the issue early next week.

There have been a dozen recess appointments to the Supreme Court, nine of which took place before the Civil War, and all but one were eventually confirmed by the Senate. Dwight D. Eisenhower made three recess appointments: Earl Warren, William Brennan and Potter Stewart.

Under a unanimous 2014 ruling, the Supreme Court gave broad discretion to the Senate when it came to defining a recess. The president can still make recess appointments when the Senate is away, but recent congressional leaders have foreclosed that possibility by scheduling brief pro forma meetings that keep the Senate in session.

White House officials continued to consult with lawmakers from both parties Wednesday on Capitol Hill, though it was unclear how the administration could come up with a candidate acceptable to Republicans. Even jurists who had won praise from GOP senators in the past — such as Judge Sri Srinivasan of the U.S. Court of Appeals for the District of Columbia Circuit — cannot count on Republican support.

While the majority of candidates under consideration are federal appellate judges — and Obama has a large number to choose from, given his success in appointing many to the bench during his more than seven years in office — there is one district judge whose name has surfaced in recent days: Ketanji Brown Jackson. Jackson, a 45-year old African American was confirmed unanimously by the Senate for the U.S. District Court for the District of Columbia in 2013. She is related by marriage to House Speaker Paul D. Ryan (R-Wis.), who testified on her behalf in December 2012.

Cruz, who joined 96 other senators in backing Srinivasan’s appointment to the appeals court less than three years ago, said Wednesday that Obama should not appoint any justice in an election year. “Voting for a candidate for the D.C. circuit is very different from confirming someone to the U.S. Supreme Court,” he said during a campaign stop in Seneca, S.C.

Meanwhile, the White House announced Wednesday that the president and first lady will pay their respects to Scalia on Friday as he lies in repose in the Supreme Court but will not attend his funeral Mass on Saturday. Vice President Biden and his wife, Jill, will attend the service, at Washington’s Basilica of the National Shrine of the Immaculate Conception.

Correction: A previous version of this story misstated how long a recess appointee may serve. Those appointments continue until the end of the next congressional session after the appointment is made.

Paul Kane, Kelsey Snell, Elise Viebeck and Katie Zezima contributed to this report.