Story highlights Obama: 'The Constitution is pretty clear about what is supposed to happen now'

Republicans warned that Obama's nominee should not even expect a vote before the President leaves office

(CNN) President Barack Obama vowed on Tuesday to name an "indisputably" qualified Supreme Court nominee and lashed out at Republicans who he said demand a strict interpretation of the Constitution -- except regarding his right to propose a new justice.

The President staked out a tough position after Republicans warned he would not get a vote on his eventual nominee to replace the late Justice Antonin Scalia. The GOP is arguing that filling the seat on the nation's highest bench should be left to the next president.

"The Constitution is pretty clear about what is supposed to happen now," Obama said during his first press conference since Scalia's passing over the weekend.

Obama took a swipe at Republicans by saying he was amused to hear some in the party describe themselves as "strict interpreters" of the Constitution but dispute the idea that he has the right to get a hearing for a Supreme Court nominee.

"I am amused when I hear people who claim to be strict interpreters of the Constitution suddenly reading into it a whole series of provisions that are not there," he said. "I am going to present somebody who indisputably is qualified for the seat and any fair minded person, even somebody who disagreed with my politics would say would serve with honor and integrity on the court."

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