The Trump administration Sunday reaffirmed the president's insistence that he would allow a partial shutdown of the federal government if Congress does not provide $5 billion to build a wall along the U.S.-Mexico border, with senior adviser Stephen Miller calling it a "fundamental issue."

"At stake is the question of whether or not the United States remains a sovereign country," Miller told CBS News' "Face The Nation." "The Democrat Party has a simple choice. They can either choose to fight for America's working class or to promote illegal immigration. You can't do both."

"At stake is the question of whether or not the United States remains a sovereign country. The Democrat Party has a simple choice. They can either choose to fight for America's working class or to promote illegal immigration. You can't do both." — Stephen Miller, senior adviser to President Trump

When asked if the administration was willing to allow parts of the government to cease operation at midnight Friday if the wall is not funded, Miller answered: "If it comes to it, absolutely."

On NBC News' "Meet The Press," Senate Minority Leader Chuck Schumer, D-N.Y., insisted that President Trump "is not going to get the wall in any form."

"President Trump should understand, there are not the votes for the wall in the House or the Senate," Schumer said. "Even the House, which is a majority Republican, they don't have the votes for his $5 billion wall plan ... And we should not let a temper tantrum, threats, push us in the direction of doing something that everybody, even our Republican colleagues, know is wrong."

Trump said last week he would be "proud" to have a shutdown to get Congress to approve a $5 billion down payment to fulfill his campaign promise to build a wall on the U.S.-Mexico border. Still, the president doesn't have the votes from the Republican-controlled Congress to support funding for the wall at that level.

Schumer and House Minority Leader Nancy Pelosi, D-Calif., have proposed no more than $1.6 billion for border fencing upgrades and other security measures -- but not a wall -- as outlined in a bipartisan Senate bill. Democrats also offered to keep funding at its current level, $1.3 billion.

"[Republicans] should join us in one of these two proposals, which would get more than enough votes passed and avoid a shutdown," Schumer said. "Then, if the president wants to debate the wall next year, he can. I don't think he'll get it. But he shouldn't use innocent workers as hostage for his temper tantrum to sort of throw a bone to his base."

Both parties in Congress have suggested that Trump would need to make the next move to resolve the impasse. The House is taking an extended weekend break, returning Wednesday night. The Senate returns Monday after a three-day absence.

Trump neither accepted nor rejected the Democrats' proposal as of Friday, according to the Democrats, telling them he would take a look. Trump would need Democratic votes either now or in the new year, for passage.

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Sen. John Barrasso, R-Wyo., told "Face The Nation" that Republicans remained hopeful they could come up with a proposal that would be acceptable to Trump and pass both chambers. He suggested that could take the form of a stopgap bill extending funding until January or a longer-term bill including money for border security.

"There are a lot of things you need to do with border security," he said. "One is a physical barrier but also the technology, the manpower, the enforcement, all of those things, and our current laws are in some ways an incentive for people to come to this country illegally, and they go through great risk and possibly great harm."

Appearing on ABC News' "This Week," Sen. Susan Collins, R-Maine, urged senators to revisit a bill she helped push earlier this year that would provide $2.5 billion for border security, including physical barriers as well as technology and border patrol agents.

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"There's absolutely no excuse to shut down government on this issue or any other issue," said Collins, who added of her proposal: "I hope it would be good enough for the president ... There's a compromise and people will come to the table in good faith on both sides. We have to prevent a government shutdown."

The Associated Press contributed to this report.