GOP senator: Obama's SCOTUS nominee must be a 'consensus' choice

Sen. Lindsey GrahamLindsey Olin GrahamSenate GOP: Legislation to protect Mueller not needed Cornyn: Hearing on McCabe firing would be 'appropriate' McCain: Mueller must be allowed to finish investigation 'unimpeded' 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.

"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 CruzOvernight Tech: Facebook faces crisis over Cambridge Analytica data | Lawmakers demand answers | What to watch for next | Day one of AT&T's merger trial | Self-driving Uber car kills pedestrian The case for a new branch of the military: United States Space Force The problem with hindsight MORE (R-Texas) and Marco RubioMarco Antonio RubioRubio: McCabe 'should've been allowed to finish through the weekend' For Tillerson, bucking Trump became a job-killer At least six dead after pedestrian bridge collapses on cars in Florida 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 ClintonTrump adds to legal team after attacks on Mueller Press: You can’t believe a word he says Feehery: March Madness MORE specifically.