Mr. Trump spent the weekend at his golf retreat in Bedminster, New Jersey - it wasn't immediately clear if he took any of that time to meet with, or talk to, possible candidates for the spot on the Supreme Court.
As for the nomination fight - which started stirring last week - the President expressed confidence.
"I think we're going to have a lot of support," the President said in an interview with Fox News that was aired on Sunday morning, as Mr. Trump is expected to spend coming days trimming down his list of 25 judges, before making a final choice.
"I’m going to pick somebody who’s outstanding," the President declared.
In the interview, Mr. Trump expressed confidence that the confirmation process would go "quickly" - as Senate Republicans envision a repeat of the 66 day approval for Justice Neil Gorsuch.
Here is a possible time line:
+ President Trump announces nominee on July 9.
+ While Mr. Trump goes to Europe for NATO summit and a meeting Russian leader Vladimir Putin, the President's nominee then starts visits with Senators on Capitol Hill.
+ Those meetings with Senators go for a few weeks.
+ Senate Judiciary Committee holds a week of hearings in mid-August.
+ Then it takes another two weeks before a committee vote (that vote could happen in late August, or even early September).
+ Senate floor debate starts after Labor Day .
+ Full Senate vote happens in mid to late September.
+ New Justice is on the bench for the start of the 2018-2019 term on the First Monday in October.
If the President is able to repeat the 66 day process for Justice Gorsuch - 66 days from July 9 is September 13. So, that would seem to be a confirmation time line that could work - barring any nomination calamity.
As for Democrats - all they can do in the Senate right now is raise questions about certain issues - like Roe v. Wade and abortion - and wait to see whether any Republicans break ranks with the President over his pick.
"Now, some of the people on the list, I have not vetted at all at this point," said Sen. Susan Collins (R-ME), as Collins and Sen. Lisa Murkowski (R-AK) are being targeted by Democrats in this nascent nomination fight, especially over the issue of abortion.
With filibusters no longer an option in the Senate, it all boils down to who has the most votes for Mr. Trump's Supreme Court nominee.
Three Democrats voted for Justice Neil Gorsuch - Sen. Joe Donnelly (D-IN), Sen. Joe Manchin (D-WV), and Sen. Heidi Heitkamp (D-ND) - they will get a lot of attention again this time, as they met with President Trump last Thursday night.
"I think we're going to have support from Democrats," Mr. Trump said on Sunday.
Even one Democratic vote in the Senate could make a big difference.
Here is the President's list of 25 judges that he says he will consider for the U.S. Supreme Court:
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