In calling on Mr Trump to reopen government while negotiations on border security continue, Democrats have emphasised there are families unable to pay bills due to absent wage payments.
Transport Security Administration employee Brian Turner told the BBC he might have to look for another job if the shutdown continued.
"We must be champions of the middle class and all those who aspire to it - because the middle class is the backbone of our democracy", she said.
"Could be a long time or could be quickly", Trump said during lengthy comments at a Cabinet meeting at the White House, his first public appearance of the new year. Democratic leaders can play good cop on impeachment and Tlaib and the freshmen can play bad cop.
Trump is demanding billions of dollars to build his wall along the U.S. Border with Mexico, which the Democrats have refused.
On Thursday, Trump tried to keep the pressure on Democrats, even as they gained significant new power with their takeover of the House of Representatives at the start of a new Congress.
"Many of those people, most of those people, that really have not been and will not be getting their money in at this moment, those people in many cases are the biggest fan of what we're doing", he added.
Talks to end the government shutdown - led by Vice President Mike Pence - again ended without a breakthrough on Saturday.
Meanwhile, while Ms Pelosi has been cautious about calls to impeach Mr Trump, other lawmakers have pushed for this, including Ms Tlaib, who also attracted controversy for using offensive language to describe the president.
"I was a little shocked, that's a little extreme, for people of that stature you know", said Mario Gjolaj from Onassis Coney Island.
The House passed two measures that would re-open government agencies whose funding had lapsed, but provide no money for a border wall demanded by Donald Trump.
In a television appearance Friday night, House Speaker Nancy Pelosi blamed Senate Republicans for enabling the president.
The legislation is designed as a companion to a bipartisan bill that was approved by the Senate Judiciary Committee in April.
Mr McConnell called the Democrats' move a "total nonstarter" and a "political sideshow".
"We have to wait and see what happens with the Mueller report", Pelosi told "Today" on Thursday morning.
Mrs. Pelosi then argued that Mrs. Tlaib's rhetoric is culturally inconsequential while the president's statements carry weight.
They are all but dead on arrival in the Senate, where the Republican leadership has vowed not to bring them up for a vote because they do not pass muster with the president.
But some Republican senators - particularly those up for re election in 2020 - are demanding a solution. "We can not undo the trauma that he is causing to our people". She refused to repeat them because "she doesn't want her kids to hear them".
"I think some of our new members probably don't realize that you are always on, that when you are a member of Congress, there's always someone listening", said Rep. Jan Schakowsky.
