Attorney General Jeff Sessions on Sunday led the Sunday show charge, expressing confidence the border wall would be funded.
"I can't imagine the Democrats would shut down the government over an objection to building a down payment on a wall that can end the lawlessness," Sessions said on ABC's "This Week."
He said he doesn't expect the Mexican government to "appropriate money" for the wall, but added there are ways "we can deal with our trade situation to create the revenue to pay for it."
"We're going to get it paid for one way or the other," Sessions said on ABC's "This Week" when asked if there is any evidence Mexico will pay for the wall as Trump promised on the campaign trail.
Sessions said the administration's goal is to put an end to illegality and "create a lawful system of immigration where people apply to come here, they wait their turn."
Building a wall along the country's southern border will help the president to fulfill his promise to the American people, he said.
"That's what they want," he said. "And I believe Congress will eventually deliver."
Homeland Security Secretary John Kelly said the president will likely be "insistent" that an upcoming spending bill includes funding for his wall.
"I think it goes without saying that the president has been pretty straightforward about his desire and the need for a border wall," Kelly said on CNN's "State of the Union."
"So I would suspect — he'll do the right thing for sure — but I suspect he will be insistent on the funding."
White House chief of staff Reince Priebus said he thinks the government can avoid a shutdown and expressed confidence a bill that is "satisfactory" to the president will pass.
Progress has already been made "in regard to getting money for border security," he said on NBC's "Meet The Press."