WASHINGTON — President Barack Obama is challenging Republicans to live up to their avowed adherence for the Constitution and agree to vote on his nominee to replace the late Supreme Court Justice Antonin Scalia. A key Republican is leaving the door open to taking the first step.

Despite widespread GOP insistence that he leave the decision to the next president, Obama said Tuesday he had no intention of abdicating his responsibilities before leaving office early next year. He chidingly told the Senate he expects “them to do their job as well.”

“The Constitution is pretty clear about what’s supposed to happen now,” Obama said before returning to Washington from California.

Fallout from Scalia’s unexpected death overshadowed Obama’s two days of summitry with Southeast Asian leaders. Obama pledged to nominate a candidate “indisputably” qualified, but Republican leaders have threatened to refuse to hold hearings or a vote on his pick to replace the conservative Scalia.

Yet there were hints that at least some Republicans might come around. Senate Judiciary Chairman Charles Grassley, R-Iowa, said he would wait “until the nominee is made before I would make any decision” about holding hearings.

With the looming nomination creating ripples in the presidential campaign, Obama sought to broaden his argument by calling the dispute emblematic of years of escalating partisan hostilities over judicial nominations. He lamented a new normal in which “everything is blocked” even when there’s no ideological or substantive disagreement — and conceded that Democrats are not blameless.

“This would be a good moment for us to rise above it,” Obama said.

Since Scalia’s unexpected death over the weekend, White House lawyers and advisers have been scrambling to identify potential replacements.