GOP senator: Obama's SCOTUS nominee must be a 'consensus' choice
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Sen. Lindsey GrahamLindsey Olin GrahamSenators huddle on Russia sanctions as tensions escalate Juan Williams: It's Trump vs. McConnell for the GOP's future Biden's year two won't be about bipartisanship  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 CruzRafael (Ted) Edward CruzHow Cruz Supreme Court case could lead to unlimited anonymous election spending Poll: Trump leads 2024 Republican field with DeSantis in distant second The politics of 'mind control' MORE (R-Texas) and Marco RubioMarco Antonio RubioPut partisan politics aside — The Child Tax Credit must be renewed immediately These Senate seats are up for election in 2022 Lawmakers press Biden admin to send more military aid to Ukraine 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 Diane Rodham ClintonThe Armageddon elections to come Poll: Trump leads 2024 Republican field with DeSantis in distant second The politics of 'mind control' MORE specifically.