"It was done in such a sloppy and careless way . . . It almost seems like back of the envelope," Senate Minority Leader Charles Schumer said on NBC's Today show about the ban. He added that he planned to call for the immediate consideration of a bill by Senator Dianne Feinstein to rescind the order.
But there is insufficient GOP support to outright reverse Trump's ban.
While a handful of Republican senators have expressed concerns, just eight - John McCain, Jeff Flake, Lindsey Graham, Ben Sasse, Susan Collins, Cory Gardner, Dean Heller, and Jerry Moran - have said they're opposed to the ban, according to a Washington Post whip count of GOP lawmakers.
If those Republicans joined the 48 members of the Senate Democratic caucus in supporting the bill, that's still not enough to clear various procedural hurdles that require 60 votes to overcome.
With legislation unlikely to advance, Democrats will quickly shift back to Trump's Cabinet nominees, who have occupied much of the Senate's time so far this year. Two nominees - Rex Tillerson, to serve as secretary of state, and Elaine Chao, to serve as transportation secretary - are set for floor votes this week. But aides said that Democrats plan to draw out consideration of them for as long as possible, meaning that scheduled plans to confirm Chao and Tillerson tomorrow should stretch into Thursday.
Four committees are scheduled to vote on five more Cabinet nominees tomorrow and virtually all Democrats are expected to vote against them.
Among the picks up for consideration are Senator Jeff Sessions for attorney general. Not one Democrat on the Senate Judiciary Committee has said they plan to vote for Sessions. In the full Senate, just one Democrat, Senator Joe Manchin has suggested that he will vote for Sessions.
The Senate's health and education panel is also set to approve GOP power broker Betsy DeVos to serve as education secretary, but Democrats have strongly objected to her amid concerns that she hasn't answered hundreds of written questions or made plans to divest herself from holdings in firms that do business with the Education Department.
In a sign of likely widespread opposition to Trump's Cabinet appointments among Democrats, Schumer also announced on Facebook that he would be opposing a total of eight nominees that his caucus had identified as top targets at the beginning of the year.
He repeated his plans to vote against Tillerson, Sessions and DeVos, but added that he would also vote against Trump's picks to lead the Office of Management and Budget, the Environmental Protection Agency and the departments of Health and Human Services and Labor, because they "have repeatedly shown they will not put the American People or the Laws of our nation first".
Despite the opposition of Schumer and others, Democrats are unlikely to derail the confirmation of any Trump nominees. While they can use procedural tactics to slow down the length of time it takes to confirm a pick, just 51 senators are needed to confirm a nominee. Republicans enjoy a 52-seat majority in the Senate.
Regardless, liberal organisations are intensifying the pressure on Democratic lawmakers.
On a call organised by MoveOn.org yesterday, American Civil Liberties Union political director Faiz Shakir encouraged activists to demand a Senate slowdown until Trump's executive orders on immigration and refugees were tacked back.
Even if Democrats fail to make their point on the Senate floor, they hope to galvanise growing public concern by holding a rally outside the US Supreme Court today.
Even when some senators showed up at airports this weekend to join protests or attempt to free travellers subject to the travel ban from detention, they were challenged on their votes for Trump nominees.
Amid the Democratic outcry, Trump and his aides strongly defended the ban and faulted Democrats for trying to "obstruct" his Cabinet nominees.
"We actually had a very good day yesterday in terms of homeland security," Trump said today at a White House event. During a meeting with small business leaders, he blasted Democrats for delaying the confirmation of his nominees "for political reasons. Just politics".
Trump singled out Schumer for tearing up at a news conference yesterday as he denounced the travel ban.
"I'm going to ask him who was his acting coach, because I know him very well. I don't see him as a crier," Trump said.
While not known to be as emotional as former House Speaker John Boehner - a frequent crier - Schumer has been known to tear up in public before.