GOP senator: Obama's SCOTUS nominee must be a 'consensus' choice
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Sen. Lindsey GrahamLindsey Olin GrahamTrump digs in amid uproar on zero tolerance policy Senate passes 6B defense bill Justice IG says report doesn’t assess ‘credibility’ of Russian probe 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 CruzMcCain calls on Trump to rescind family separation policy: It's 'an affront to the decency of the American people' Cruz announces bill to end separation of immigrant families The Hill's 12:30 Report — Sponsored by Delta Air Lines — Furor grows over child separation policy MORE (R-Texas) and Marco RubioMarco Antonio RubioHillicon Valley: Supreme Court takes up Apple case | Senate votes to block ZTE deal | Officials testify on Clinton probe report | Russia's threat to undersea cables | Trump tells Pentagon to create 'space force' | FCC begins T-Mobile, Sprint deal review Feehery: Betting on Trump Senate votes to block Trump's ZTE deal 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 ClintonKoch brothers group won't back Stewart in Virginia Giuliani says his demand for Mueller probe to be suspended was for show Poll: GOP challenger narrowly leads Heitkamp in North Dakota MORE specifically.