WASHINGTON — President Obama on Wednesday said he hoped and expected that the Senate would consider the Supreme Court nominee he selects once he makes his choice, despite a vow by Republicans this week that they would not even meet with his candidate.

“I recognize that the politics are hard for them, because the easier thing to do is to give in to the most extreme voices within their party and stand pat and do nothing, but that’s not our job,” Mr. Obama told reporters in the Oval Office after a meeting with King Abdullah II of Jordan. “Our job is to fulfill our constitutional duties.”

Mr. Obama predicted that Senator Mitch McConnell of Kentucky, the majority leader, and other Republicans would not be able to sustain their refusal to acknowledge or act on his nominee, adding that in his private conversations with some of them on the matter, it was clear to him that they were not comfortable with that stance.

“They’re pretty sheepish about it,” the president said.

He added, “I think it will be very difficult for Mr. McConnell to explain, if the public concludes that this person is very well qualified, that the Senate should stand in the way simply for political reasons.”