Getting dollars for a border wall was always going to be an uphill task for Trump. The first vote would be on a financial services measure, which funds the Treasury Department, IRS, Securities and Exchange Commission, and other government agencies.
Moreover, Chamberlain argued, in order to overrule an emergency declaration, both the House and the Senate would have to adopt a joint resolution with veto-proof majorities.
The president has previously suggested his definition of "wall" is flexible, but Democrats view the whole idea as immoral and ineffective, and prefer other forms of border security.
The shutdown, which is threatening to become the longest in USA history, is affecting about 800,000 federal workers, many of whom will soon miss their first paycheck, and has curtailed the functions of numerous government agencies.
Asked about it on "Fox News Sunday", White House Press Secretary Sarah Huckabee Sanders said "whatever action he takes will certainly be lawful, and we're looking at every option". One of the officials - neither was authorised to speak publicly - said no additional meetings were scheduled. President Donald Trump later tweeted that "not much headway" was made, while Pence called the meeting "productive". "If we don't have border security, we are going to be crime-ridden and it's going to get worse and worse".
Not all Republicans agree with Trump's insistence on keeping many government agencies shuttered until the border debate is resolved. Trump said Democrats "don't like concrete, so we'll give them steel".
He has insisted that the wall is essential to addressing illegal immigration and drug trafficking, while Democrats have slapped the proposal as an "inefficient, unnecessary and costly" solution to strengthening border security.
Democrats and Republicans have been continuing to meet for negotiations as the shutdown drags on, but it seems these talks haven't led to any real progress.
A source in the meeting said the weekend talks were good only in the sense that they got a more precise sense of what the administration wanted.
Adding to concerns, federal workers might miss this week's pay cheques.
"It'll be discussed", he said on NBC.
However, opponents would nearly certainly accuse him of presidential overreach and respond with court challenges. "So that's a non-starter", Rep. Adam Schiff, D-Calif., told CNN's "State of the Union" on Sunday.
The president said that a wall or a barrier must be built along the US southern border with Mexico, while signaling a willingness to accept a steel barrier instead of a concrete wall by saying that "steel instead of concrete is fine".
Mr. Trump now says he'll accept "steel slats" instead of a "concrete" wall, although that change doesn't appear acceptable to Democrats. He's not building a wall anymore, ' that should help us move in the right direction, ' Mulvaney said on NBC's 'Meet the Press'.
Pressed about the terrorism claims during an impromptu Rose Garden news conference last week, Department of Homeland Security Secretary Kirstjen Nielsen pointed to another statistic: that more than 3,000 "special interest aliens" have tried to enter the USA through the southern border, suggesting those individuals "have travel patterns that are identified as terrorist travel patterns or they have known or suspected ties to terrorism".