Leonard Leo, who is advising Trump on his pick to fill the seat of Justice Anthony Kennedy, said two names on the president's shortlist - Raymond Kethledge and Thomas Hardiman - had less established conservative records, making it harder to line up support should they be selected.
Trump spoke to reporters Sunday afternoon before returning to Washington from a weekend at his private golf club in New Jersey, where he deliberated his decision amid furious lobbying and frenzied speculation.
Hardiman, who was runner-up to Neil Gorsuch as the president's Supreme Court pick past year, made a comeback on Trump's shortlist this weekend in part because of the president's sister, Judge Maryanne Trump Barry, who serves with Hardiman on the U.S. Court of Appeals for the Third Circuit.
"He could throw a dart on that list" and conservatives would be happy.
Trump is also believed to be studying Brett Kavanaugh, 53, of the US Court of Appeals for the DC Circuit and a Yale Law School graduate.
By installing Gorsuch and another, similar candidate on the court, Trump can tell conservative voters that he kept his promises and give them a reason to solidify his electoral coalition. If the decision is made permanent, it would lead to higher premiums.
Hardiman could also have one important advocate.
Pompeo dismisses North Korea's 'gangster' accusations
Pompeo is in Tokyo to brief his Japanese and South Korean counterparts on the talks, which he has characterised as productive. State Department spokesperson Heather Nauert tweeted that Pompeo spoke briefly before leaving Pyongyang.
Cornyn spoke shortly after Senate Democratic Leader Chuck Schumer said any of Trump's likely nominees poses a threat to the Affordable Care Act and a woman's right to have an abortion. In a recent case involving abortion and immigration, he wrote a decision that temporarily barred a pregnant teenager in immigration custody from obtaining an abortion.
The White House would love to have the Democrats' votes for confirmation. That means President Trump should select anyone but Kethledge or Hardiman. Susan Collins, of ME, to speak out, told Stephanopoulos last week that a candidate who would overturn Roe v. Wade "would not be acceptable", because it indicates an "activist agenda" she didn't want to see in a judge. She rocketed to the top of Trump's earlier list of 25 Supreme Court candidates after her performance during her confirmation hearing last fall, when Democrats cited her deep Catholic faith as a potential problem.
Democrats see the seat being vacated by Justice Kennedy, a conservative judge who sometimes sided with the court's liberal wing, as critical to maintaining abortion rights and key provisions of former President Barack Obama's healthcare plan.
Conservatives will focus on moderate Democrats running for re-election in Trump country, such as Indiana's Joe Donnelly, North Dakota's Heidi Heitkamp and West Virginia's Joe Manchin. We don't know who this nominee is going to be yet.
"I don't think anyone should expect me to simply vote yes for this nominee just simply because my state may be more conservative than others", Mr. Jones said Sunday on CNN's "State of the Union".
"I'm very confident with this president's enthusiasm and with Leader [Mitch] McConnell's enthusiasm that they can get anybody confirmed", Leo told ABC News Chief Anchor George Stephanopoulos on "This Week" Sunday.
While the president has been pondering his choice, his aides have been preparing for what is expected to be a tough confirmation fight.