Flowers are placed in front of the U.S. Supreme Court. The death of Justice Antonin Scalia, a towering conservative voice on the court, has triggered a political showdown over his succession. (Brendan Smialowski/AFP via Getty Images)

White House officials began sifting through their pool of potential nominees for the newly vacant seat on the nation’s highest court Sunday, girding for battle with Republicans who are insisting that President Obama leave the choice of a new justice to his successor.

But Obama pledged Saturday to nominate a replacement for Justice Antonin Scalia, who died suddenly Saturday during a hunting trip, and on Sunday, principal deputy press secretary Eric Schultz said the White House expected the Senate to give that nomination appropriate consideration when the time came. Schultz said the White House would not rush on a nomination this week, given that the Senate will be in recess.

“As the president said last night, he takes his constitutional responsibility seriously and will approach this nomination with the time and rigor required,” Schultz said. “At that point, we expect the Senate to consider that nominee, consistent with their responsibilities laid out in the United States Constitution.”

But it was clear Sunday that any nominee would become the focus of an epic debate that promises to tie the Senate in knots and dominate the 2016 election campaign.

Sen. Ted Cruz (Tex.), one of the GOP’s leading presidential candidates, vowed Sunday to filibuster any nominee the White House sends to Capitol Hill. “This is a 5-4 court,” Cruz said. “This next election needs to be a referendum on the Court. The people need to decide.” Speaking on ABC’s “This Week” he added: “We should not allow a lame duck to essentially capture the Supreme Court in the waning months of his presidency.”

Time spent considering Supreme Court nominees

While Obama suggested Saturday that the Senate is constitutionally obligated to consider a replacement for Scalia as soon as possible, Republicans have forcefully rejected that argument. Cruz, appearing on NBC’s “Meet the Press,” said the Senate is “not remotely” required to consider such a nomination.

And Sen. Marco Rubio (R-Fla.), another prominent presidential hopeful, used the moment to try to rally voters to his side by promising that he would replace Scalia with a conservative justice like the one they have just lost. “When I’m president of the United States, I’ll nominate someone like Justice Scalia,” Rubio said in an appearance on CNN.

Obama’s problems extend beyond the obviously heated campaign rhetoric. Congressional Republicans have staked out similar positions, warning the president that any nomination he sends to the Senate will face delay or defeat, and they have the numbers to back up their threats.

To overcome a GOP filibuster, Obama will need to win the support of all 46 members of the Democratic caucus and at least 14 Republicans to reach the 60-vote threshold to advance a nomination to final approval. In 2013, when Democrats were in the Senate majority, they forced a controversial rules change, invoking the so-called “nuclear option,” to allow the approval of ­lower-court judges by a simple majority. Those changes did not apply to Supreme Court nominations, which can be filibustered, and are therefore subject to the higher 60-vote threshold. Republicans were furious about the 2013 changes, and that residual anger could be a huge obstacle for any Obama nominee.

Sen. Lindsey O. Graham (R-S.C.) warned in an interview that the Democrats’ decision to change the judicial confirmation rules has made it nearly impossible to confirm a Supreme Court nominee under the current president. “I voted for every Supreme Court justice nominated by [George W.] Bush and Obama. I believe the Senate should be deferential to qualified picks,” Graham said Saturday in an interview. “But I did tell [then-Senate Majority Leader] Harry Reid and the president that the consequence of changing the rules in the Senate to pack the court will come back to haunt them.”

Graham said he warned Obama directly: “You’re leading the effort to turn the rules upside down, to pack the [Supreme] Court. . . . There will be consequences, and I’ll find it very hard for me” to support a nominee now that “we are inside of a year” before the next president’s swearing-in.

Washington Post reporter Robert Barnes explains where the Supreme Court stands after the death of Justice Antonin Scalia and how the vacant seat will impact the presidential election. (Whitney Leaming/The Washington Post)

Administration officials would not provide further details about the selection Sunday, but in the past the president has taken about a month to forward a name to the Senate once a vacancy opened up on the Supreme Court. It took him that long to nominate Justice Sonia Sotomayor after David Souter announced his retirement, and to pick Justice Elena Kagan after John Paul Stevens said he was stepping down.

Some hopeful Democrats now see the nomination of a sitting senator as the best chance Obama has to seat another justice on the Supreme Court before leaving office. In an interview Saturday, Sen. Patrick J. Leahy (Vt.), the top Democrat on the Judiciary Committee, repeated his previous calls for a justice with a different background than serving on federal appellate courts.

“We’ve got to start getting some nominees from outside the judicial monastery,” he said, adding it could be a politician or a prosecutor with a strong legal background. “Somebody who can handle the law.”

There are several Senate Democrats who fit that description, including Amy Klobuchar (Minn.), Sheldon Whitehouse (R.I.), Christopher A. Coons (Del.) and Richard J. Durbin (Ill.). But individuals who have spoken with the White House about the nomination process, who spoke on the condition of anonymity because no final decisions had been made, said the president is interested in a candidate who is young enough to serve an extended period of time. Only two of those senators — Klobuchar, at 55, and Coons, at 52 — are younger than 60, the age Justice Ruth Bader Ginsburg was when she was nominated.

The president has also prized diversity in his judicial picks, and the federal bench remains fertile ground for nominees of color as well as those who are women. Although Obama has installed fewer federal appellate judges than either Presidents Clinton or George W. Bush, he has put enough nominees on the bench that Democratic appointees are in the majority on nine of the nation’s 13 circuit courts.

In that group, the 9th Circuit’s Paul J. Watford, a 48-year-old African American, and Sri Srinivasan, a 48-year-old judge on U.S. Court of Appeals for the District of Columbia Circuit who would be the first South-Asian American on the Supreme Court, would be the leading contenders. Others include the D.C. Circuit’s Patricia Ann Millett, 52, and Jane L. Kelly, 51, a judge on the 8th Circuit who was confirmed 96 to 0 with the support of Senate Judiciary Committee Chairman Charles E. Grassley (R-Iowa).

Merrick B. Garland, a former prosecutor who serves as the D.C. Circuit’s chief judge, is a possibility because he is well liked by Republicans.

If Republicans show they are determined to block a nominee under any circumstances, it may complicate the administration’s calculations and could spur the president to make a more adventuresome choice. That could include judges such as Lucy H. Koh, the first Asian American district judge in the Northern District of California, or Monica M. Márquez, who is the first Latina and first openly gay justice on the Colorado Supreme Court. Or the president could draw from the ranks of his own administration, where Attorney General Loretta E. Lynch, Solicitor General Donald B. Verrilli Jr. and Homeland Security Secretary Jeh Johnson are all possibilities.

Charles Geyh, a professor at Indiana University’s Maurer School of Law, said the uncertainty surrounding the confirmation process might prompt some candidates to bow out, and it would favor someone with a political background “with some sort of cachet on both sides of the aisle, especially with Republicans.”

Geyh, who is the author of “Courting Peril: The Political Transformation of the American Judiciary,” said that a current or former elected official would probably have a greater tolerance for undergoing what is likely to be a difficult ordeal and would mean there’s at least “a snowball’s chance in hell this would work.”

Robert Barnes contributed to this report.