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)

Conservative and liberal advocacy groups are gearing up for a ferocious political brawl over President Obama’s pick to fill the Supreme Court vacancy created by the weekend death of Justice Antonin Scalia, and already the battle is spilling from the presidential campaign into some of the nation’s most hotly contested Senate races.

White House deputy press secretary Eric Schultz repeated Monday that the president intends to “fulfill his constitutional responsibility” by nominating a new justice and predicted that Senate Republicans, despite their current loud opposition, will ultimately hold a confirmation hearing and vote for the nominee.

“This is not the first time the Republicans have come out with a lot of bluster only to have reality sink in,” Schultz said. “We need a fully staffed Supreme Court.”

Schultz quoted President Ronald Reagan, who pressed for a vote on his Supreme Court nominee Anthony M. Kennedy, who was confirmed in 1988: “Every day that passes with a Supreme Court below full strength impairs the people’s business in that crucially important body.”

But across the board, Republicans have argued that Obama should allow his successor to make the pick and that they would block any attempt to confirm a new justice this year.

One consideration that may force Republicans to recalibrate their strategy is the prospect of political damage to some of the embattled Senate incumbents up for reelection this fall. Sens. Kelly Ayotte (N.H.), Ron Johnson (Wis.) and Rob Portman (Ohio), all Republicans in swing states, have called for the Senate to disregard any Obama nominee. Other Republicans in tight races have remained silent so far.

Democrats see a potential confirmation battle as an opportunity to put Republicans on the defensive and as a wedge issue that could help them retake control of the Senate. In Ohio, former Democratic governor Ted Strickland, who is vying for his party’s nomination to challenge Portman, said Monday that by opposing an Obama nominee, Portman was “failing to do his job, shirking his responsibilities to our nation, jeopardizing the institutions of our democracy and engaging in exactly the kind of dysfunctional behavior that frustrates Ohioans about Congress.”

P.G. Sittenfeld, a Cincinnati City Council member running against Strickland in the Democratic primary, declared Monday that Portman was advocating actions that would “put the Senate in violation of both historical precedent and the clear language of the Constitution itself.”

Portman responded in a statement Monday that the next president should choose Scalia’s replacement: “With the election less than nine months away, I believe the best thing for the country is to trust the American people to weigh in on who should make a lifetime appointment that could reshape the Supreme Court for generations,” he said.

Conservative activists are drawing up plans to mobilize support and pressure lawmakers to reject any nominee.

FreedomWorks, a group that pledges to promote “smaller government, lower taxes, free markets, personal liberty and the rule of law,” said it would wage a grass-roots campaign to oppose Democrats who would “ram liberal judicial nominees through the Senate . . . occasionally with the help of unprincipled, big government Republicans.”

Carrie Severino, chief counsel and policy director for the Judicial Crisis Network and a former clerk for Justice Clarence Thomas, said conservatives are still mourning Scalia. But, she added, “if the president tries to pack the court, as it is apparent he may, then JCN will be leading the charge to delay a Senate vote until the American people decide the next president.”

Liberal groups are working hard to undercut the prevailing Republican argument that it is inappropriate for Obama to nominate a Supreme Court justice at this late stage of his presidency.

Americans United for Change, a group closely allied with the White House, is trumpeting an article written by now-Senate Majority Leader Mitch McConnell (R-Ky.) in 1970. McConnell wrote that “the Senate should discount the philosophy of the nominee” and that “the president is presumably elected by the people to carry out a program and altering the ideological direction of the Supreme Court would seem to be a perfectly legitimate part of a presidential platform.”

Nan Aron, president of the Alliance for Justice, said the sudden Supreme Court vacancy has mobilized progressive groups and broadened the coalition usually assembled for nomination fights.

“What’s unusual about this moment, and this effort, is that the community as a whole is coming together,” said Aron, whose group focuses on federal judicial nominations. “In addition to organizations focused on judicial selections, others that aren’t realize what’s at stake and are weighing in already.”

MoveOn.org and CREDO Action, liberal advocacy groups, have launched petitions calling on the Senate to fill Scalia’s seat. As of Monday evening, each petition had garnered more than 100,000 signatures.

People close to the administration expect that Obama’s choice this time will resemble his earlier ones.

“I think the best way to think about who the president might appoint is to look at who he has appointed,” said Caroline Fredrickson, president of the American Constitution Society for Law and Policy. “He has picked people who are qualified beyond question and with an eye toward making the court more diverse. I think those will be the main touchstones.”

A person close to the administration, who spoke on the condition of anonymity to protect those relationships, said the pick is likely to be someone “super-qualified” who had been confirmed by overwhelming majorities of currently sitting Republicans; that would make it difficult for the GOP to argue that the nominee is unqualified.

Meanwhile, a wall of silence went up Monday around Scalia’s final hours and the confusion after his death. Local officials in rural West Texas, where he died, spent hours trying to locate a justice of peace after his body was discovered. The justice who was eventually found, Presidio County Judge Cinderela Guevara, pronounced Scalia dead without seeing his body — which is permissible under Texas law — and declined to order an autopsy. A second justice has said that one should have been performed.

Scalia’s family opposed an autopsy, and Guevara said Sunday that she determined by telephone that Scalia died of natural causes because he was having “health issues.’’ She cited information from federal officials at the scene and a conversation she had with Scalia’s physician. She said she was awaiting a statement from the physician to complete the death certificate.

Scalia’s physician, Brian Monahan, declined to divulge any details about Scalia’s health when reached by telephone at his home in Maryland on Monday. “Patient confidentiality forbids me to make any comment on the subject,’’ he said, before hanging up.

Jerry Markon, Sari Horwitz, Lena Sun and Alice Crites in Washington, and Eva Ruth Moravec in Austin contributed to this report.