GOP senator: Obama's SCOTUS nominee must be a 'consensus' choice
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Sen. Lindsey GrahamLindsey GrahamThe Hill's 12:30 Report Back to the future: Congress should look to past for Fintech going forward CNN to host town hall featuring John McCain, Lindsey Graham MORE says he will not support a new Supreme Court nominee from President Obama unless it is a consensus choice that both parties can agree on.

The South Carolina Republican voted for both of Obama's previous nominees, Justices Elena Kagan and Sonia Sotomayor. But he said that the 2013 move by Senate Democrats to eliminate filibusters on lower-court appointees has hardened his stance about judicial nominees.

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"You better find a consensus choice — half the Republicans should be able to vote for this person," Graham said on MSNBC.

"I'm not going to let this president abuse power and have no consequences."

Justice Antonin Scalia died on Saturday at the age of 79, creating an opening on the high court in a presidential election year.

Graham did not go as far as other Republican senators, including White House hopefuls Sens. Ted CruzTed CruzBrietbart CEO reveals that Trump donors are part owners At CPAC, Trump lashes out at media Conquering Trump returns to conservative summit MORE (R-Texas) and Marco RubioMarco RubioAt CPAC, Trump lashes out at media Conquering Trump returns to conservative summit Rubio brushes off demonstrator asking about town halls MORE (R-Fla.), in calling for the decision about Scalia's successor to be left to the next president.

He said that while he voted for Kagan and Sotomayor because both were well-qualified despite his disagreements with their policies, he would not extend that courtesy to Obama's next appointee. 

Still, Graham, a former White House contender himself, said he would still be open to voting for a well-qualified liberal appointed by a future Democratic president, naming 2016 front-runner Hillary ClintonHillary Rodham ClintonPerez to hit the Sunday shows following election victory Five takeaways from CPAC Clinton: Dems will be 'strong, unified' with Perez MORE specifically.