And with Trump's threat that he might declare a national emergency in order to grab military funding to build the wall, Democrats have even less incentive to negotiate with him. Some border security officials said they agree with his demand for a wall. The White House said money was not discussed in depth, but the administration was clear about the need for a wall and the goal of resolving the shutdown all at once, not piecemeal.
Despite public polling indicating a majority of Americans oppose the construction of a border wall, Trump and his top advisers have continued to press their case.
Trump's consideration of using emergency powers was hotly debated by those on both sides of the issue on the Sunday morning news shows.
No, what seems to be stopping Democrat leaders from working with the president on securing funding is either their extreme pandering to the left-wing of their party, at best, or their personal hatred for the president, at worse. It has to do with: The wall is an immorality between countries.
But the letter also provided a fuller picture of Trump's border demands.
Acting chief of staff Mick Mulvaney said on NBC's "Meet the Press" that if the shutdown continues into Tuesday, "then payroll will not go out as originally planned on Friday night". "He's not building a wall anymore, ' that should help us move in the right direction", Mulvaney told NBC.
Trump has insisted since the 2016 campaign that a physical barrier along the USA border with Mexico is the solution to what he sees as a crisis.
The border wall is the primary sticking point in negotiations with Democrats in the US Congress to end a partial government shutdown, which has dragged on for 17 days.
A further complication: Trump's long practice of contradicting his aides makes it hard for anyone else to negotiate on his behalf.
Democrats would likely demand other concessions, like protections for immigrants brought to the United States as children, otherwise known as Dreamers, or changes to other spending provisions.
Later in the afternoon, Trump told reporters, "We're looking at a national emergency because we have a national emergency". "I don't know what he's basing this on, but he's faced so many lawsuits when he ignores the law and ignores tradition and precedent", Mr Durbin said on CBS' "Face the Nation".
The Republican president has refused to fully fund the government until he gets $5.6 billion (£4.4 billion) for a US-Mexico border wall.
Trump, a former NY businessman, said he could relate to the workers who would have trouble paying bills because of the shutdown and threatened, again, to declare a national emergency as an alternative way to build the wall, depending on the outcome of talks in the coming days.
Trump will make that speech.
A day earlier, the president had tweeted that he didn't care that "most of the workers not getting paid are Democrats".
Democrats were given a list of the the administration's proposals that include the wall, and Republicans reiterated their resolve to re-open the entire government while dealing with border security, aides said.
Asked how people would manage without a financial safety net, he declared, "The safety net is going to be having a strong border because we're going to be safe".