Majority Leader Mitch McConnell said he hopes senators will give Gorsuch "fair consideration and respect the result of the recent election with an up-or-down vote on his nomination, just like the Senate treated the four first-term nominees of presidents Clinton and Obama".
In a separate video message, McConnell gushed about Gorsuch: "The President made an outstanding choice."
Just 31 current senators were in office in July 2006 when Gorsuch was confirmed without opposition to serve on the US Court of Appeals for the 10th Circuit, which has jurisdiction over all or parts of eight western states.
This time around, Gorsuch will be shepherded across Capitol Hill by former senator Kelly Ayotte of New Hampshire, a moderate Republican who lost reelection in November and will helm a team of veteran GOP political operatives overseeing the months-long confirmation fight.
Gorsuch's fate rests especially with Democrats including Senator Jeff Merkley, who suggested in recent days that he would try to mount a filibuster as payback to Republicans who blocked former President Barack Obama's final Supreme Court nominee, Merrick Garland, for almost the entirety of 2016.
"This is a stolen seat," Merkley said in a statement yesterday.
Other Democrats said their consideration of Gorsuch would now be tied to Trump's executive order temporarily barring US entry for foreign nationals from seven majority-Muslim countries and for refugees worldwide - and his decision to fire the acting Attorney general, Sally Yates, for refusing to defend the order in court.
"In light of the unconstitutional actions of our new President in just his first week, the Senate owes the American people a thorough and unsparing examination of this nomination," said Senator Patrick Leahy, a senior member of the Judiciary Committee that will consider Gorsuch's nomination.
Senator Richard Blumenthal, another member of the panel, added that he had "deep, serious concerns" about Gorsuch.
"If I conclude that Judge Gorsuch is out of the mainstream, then I will pursue every legal tool available to block his nomination," Blumenthal said.
By threatening to filibuster, Democrats could be laying the tripwire for Republicans to get rid of it entirely. Just a few years ago, it was Democrats who ended the ability to filibuster presidential appointments - with the crucial exception of Supreme Court nominees. If Merkley and other Democrats follow through on their threat, Republicans will not even have the support to bring up Gorsuch's name for a vote. It would be just the second time in modern history that a Supreme Court nominee has been filibustered.
That very plausible situation will leave Republicans with two unenviable decisions: Give up on getting Trump's pick through - or get rid of the filibuster so that a simple majority can approve the nominee.
That could pit McConnell's devotion to Senate customs and tradition against conservatives eager to see one of their ideological peers win a high court seat.
"You change the rules of the Senate, you are doing something pretty draconian," Senator John McCain said.
McConnell could also find himself in Trump's crosshairs, a fate he has avoided thus far, unlike his House counterpart, Speaker Paul Ryan. The President has said he supports changing the rules to avert a filibuster - a manoeuvre that is known on Capitol Hill as "the nuclear option" - if Democrats stand firm in resistance.
Some Democrats said they would frame their opposition to Gorsuch as more considered than Republican opposition to Garland.
Progressive groups including Democracy for America, meanwhile, demanded "total opposition to all of Trump's appointees", including Gorsuch, until Trump rescinds his travel ban.
The Centre for American Progress, a liberal thinktank, yesterday warned Democrats not to relent.
"The only reason that Trump can name this Supreme Court justice is because of the unconscionable actions by Senate Republicans in refusing to even hold a hearing" for Garland, the group said in a memo to senators. "Rewarding such behaviour by confirming a radical nominee should not even be an option for Democrats."
Neil Gorsuch
Born: August 29, 1967, in Denver, Colorado
Education: BA, Columbia University, 1988; JD, Harvard Law School, 1991; DPhil, University of Oxford, 2004
Current job: 2006-present: Judge, United States Court of Appeals for the Tenth Circuit (appointed by President George W Bush)
Job history: 2005-2006: Principal deputy, associate attorney general, U.S. Department of Justice. 1995-2005: Private law practice, Washington. 1993-1994: Law clerk, US Supreme Court. 1991-1992: Law clerk, Court of Appeals for the District of Columbia Circuit
Family: Wife, Louise; two daughters, Emma and Belinda. Gorsuch's mother, Anne Gorsuch Burford, was the first female head of the Environmental Protection Agency under President Ronald Reagan
Other accomplishments: While at Columbia, Gorsuch cofounded a newspaper, The Federalist, and a magazine, The Morningside Review
Quote: "The independence of the judiciary depends upon people in both parties being willing to serve, good people being willing to serve who are capable and willing to put aside their personal politics and preferences to decide cases and to follow the law and not try and make it." - from his 2006 confirmation hearing for the Tenth Circuit.