But "then Trump shredded the Constitution," said one senior aide familiar with ongoing strategy talks.
"We should be using our time on the floor to talk about the dangerous consequences to US national security by this executive order, we shouldn't be rushing through any confirmation votes this week," said Senator Christopher Murphy.
"We can take a pause in confirmation votes to try to get this executive order right. You know this is going to get Americans killed if we don't take our time to understand what this order is and what it's consequences are," he added.
Trump's ban also significantly deepened fissures in his already fragile relationship with congressional Republicans, with GOP leaders on Capitol Hill complaining angrily that they were not consulted before the order was issued.
At least a dozen key GOP lawmakers and aides said Trump's order took them by surprise, even as the White House insisted that it collaborated with Congress.
House Speaker Paul Ryan's political team sought to reassure donors and other supporters that the temporary ban does not amount to a "religious test". And a steady stream of Republican lawmakers released carefully tailored written statements expressing concerns about the order.
But others spoke out more forcefully. Senate Foreign Relations Committee Chairman Bob Corker said that he was not briefed before the order was signed.
"I know that they said they talked with some staffers on the Hill - not in our office," said Corker.
The disarray over Trump's fulfillment of a core campaign promise underscored the increasingly strained relationship between the new White House and the Republican congressional majority.
It comes after a rocky first week and a half punctuated by confusion over healthcare and tax reform, as well as frustration with the President obsessing over crowd size and his loss of the popular vote in November.
Asked if he was consulted in the drafting of the order, Senate Majority Whip John Cornyn, the number two Republican in the Senate said simply: "I wasn't".
Pressed on when he first learned about the order, Corker answered that it was Saturday, after it was signed. "I guess one of you guys probably told me about it - thank you for that," Corker told reporters.
Senate Democrats sought to quickly pass legislation that would rescind Trump's ban, but there was insufficient GOP support.
Confirmation delays began as well, when Democrats blocked a committee from meeting to approve Trump's nominee for treasury secretary, Steven Mnuchin, to the full Senate. The Senate Finance Committee is now expected to consider the former Goldman Sachs banker tomorrow, at the same time it will vote to approve the nomination of Congressman Tom Price to lead the Department of Health and Human Services.
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 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".
But it remained unclear just how united Democrats would remain.
The Senate voted on a key procedural step towards the nomination of ExxonMobil CEO Rex Tillerson for secretary of state, with three members of the Democratic caucus supporting him - Heidi Heitkamp, Angus King, Joe Manchin, and Mark Warner.
Senator Dianne Feinstein said she didn't think there would be further delays of Senator Jeff Sessions as attorney general; and it was unclear whether Democrats would succeed in delaying a hearing for Price.
Committees are also scheduled to meet to approve former Texas Governor Rick Perry to lead the Energy Department; Congressman Ryan Zinke to serve as interior secretary; and GOP powerbroker Betsy DeVos to serve as education secretary.
How far Democrats go will be closely watched by the liberal activists who joined them to protest against Trump's ban on the steps of the Supreme Court.
After the sun set, and Democrats made their way from the Capitol, chants of "hands too small, can't build a wall" and "build a fence around Mike Pence" alternated with "walk the walk!" - a command to the Democrats themselves.
And when House Minority Leader Nancy Pelosi, D-Calif., told the crowd, "What the president did is not constitutional," one protester retorted: "You're not doing anything if you don't stop Sessions!"
