GOP senator: Obama's SCOTUS nominee must be a 'consensus' choice
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Sen. Lindsey GrahamLindsey GrahamOversight panel demands answers on Pentagon waste report Overnight Cybersecurity: Retired general picked to head DHS | Graham vows to probe Russian election interference Overnight Tech: AT&T, Time Warner CEOs defend merger before Congress | More tech execs join Trump team | Republican details path to undoing net neutrality 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 CruzThe Hill's 12:30 Report Cruz defends Trump's Taiwan call Ark., Texas senators put cheese dip vs. queso to the test MORE (R-Texas) and Marco RubioMarco Rubio House passes water bill with Flint aid, drought relief What the 2016 election can tell us about 2018 midterms Fight over water bill heats up in Senate 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 ClintonFeinstein after dinner with Clinton: She has 'accepted' her loss Sanders: Trump is 'a pathological liar' Clintons remember John Glenn as a 'uniquely American hero' MORE specifically.