He said TSA employees should keep showing up for work while negotiations proceed in Washington.
Democrats back other border security measures aside from the wall, and their two-bill package passed Thursday includes $1.3 billion for border fencing and $300 million for other border security items such as technology and cameras.
Democrats, led by new Speaker of the House of Representatives Nancy Pelosi, consider the wall to be immoral and have declined to approve the US$5.6 billion Trump wants to make good on the signature promise of his 2016 presidential campaign.
Collins is among several Republicans uncomfortable with the shutdown.
With the talks stalled, House Speaker Nancy Pelosi, D-Calif., said House Democrats intend to start passing individual bills to reopen agencies.
A Democratic aide familiar with the meeting said Democratic staffers urged the administration to reopen the government, arguing that progress on the contentious issue of border security would be hard while the government was closed.
Trump is demanding over 5 billion US dollars in border security to deliver his signature campaign promise to build a wall along the USA southern border with Mexico, which has been strongly rejected by Democrats.
Democrats have signaled they could accept a deal that precluded a concrete wall but provided funding for a steel barrier.
The new Democrat-led House passed legislation last week that would provide full-year money for eight of nine federal departments that have faced a funding lapse of more than two weeks, and extend current-year funding for the Department of Homeland Security through February 8.
The partial government shutdown stretched into its third week due to an impasse over how much money to allocate to a wall along the U.S. -Mexico border.
Trump insists to reporters as he departs the White House for staff meetings at Camp David that he feels the pain of hundreds of thousands of federal workers who aren't being paid. "Mr. Schumer kept saying "you don't have money for a wall now" and we're showing pictures of what we're building on the border with the money we received a year ago - it's a very similar style to what the president wants to build in the future".
Trump is still digging in his heels, demanding billions for a border barrier that Democrats won't provide.
"The President's authority in this area is intended for wars and genuine national emergencies", Evan Hollander, communications director of the House Appropriations Committee, told CNN.
Trump reiterated his demand for a border wall in a series of tweets on Saturday.
Reflecting the depth of the divide, she added on CBS's "Sunday Morning" that Trump sometimes gave the impression that "he would like to not only close government, build a wall, but also abolish Congress, so the only voice that mattered was his own". Such a move would seem certain to draw legal challenges.
The U.S. leader said, "If we don't have border security, we'll be crime ridden", with people crossing into the U.S. illegally "killing our citizens".
The White House painted that offer, which Trump floated previously, as an olive branch.