Democrats oppose that step but may be unable to stop it and many Republicans are wary too.
Another user chimed in: "Everyone left you, that's why it's just you in the White House".
It signalled a shift in his stance from a day earlier when he had said he was not ready to do it "right now".
"We have a massive Humanitarian Crisis at our Southern Border", Trump tweeted.
The shutdown began on December 22, after Senate Democrats refused to vote on the appropriations bill giving $5.6 billion towards the construction of a barrier on the US-Mexico border that was approved by the Republican-majority House of Representatives.
Trump originally promised Mexico would pay for the wall, which he says is needed to stem the flow of illegal immigrants and drugs.
As a result, workers as diverse as Federal Bureau of Investigation agents, air traffic controllers and museum staff, did not receive paychecks Friday.
Lawmakers are due back in Washington from their states and congressional districts in the new week.
Of those 42 per cent who support the wall, 24 per cent say Trump should continue to demand the level of funding he has asked for, and 16 per cent say he should strike a deal with the Democrats.
"I want to give them a chance to see if they can act responsibly", Trump said.
Fight for the Future swiftly circulated a petition following Pelosi's speech, calling on Democrats including Senate Majority Leader Schuck Schumer (D-N.Y.) not to replace Trump's proposed wall-which critics say would further endanger migrant families coming to the US -with a surveillance system that would threaten their right to be protected from unlawful search and seizure.
"That is not a historical claim that I think any president or any Congress should want to make" Sen. One notable detail is that, while Democrats are unified in their belief that Trump is to blame for the government shutdown (89 percent feel that way), Republicans are a bit more split (65 percent of Republicans blame congressional Democrats but 23 percent also blame Trump).
While a national emergency would provide some legal framework for his administration to freely move funds toward construction of a barrier, it would nearly certainly face court challenges.
Graham has been among the most outspoken Republicans pushing Trump to use his authority to declare a national emergency to circumvent Congress and build the wall by tapping unspent money sitting in various government accounts, including for military construction and disaster relief. Instead, McConnell last week vowed to stand with Trump in the wall debate, after the president met with all Senate Republicans and pleaded for party unity behind his wall quest. The White House has not indicated if Trump would sign it.
Coons also took aim at Trump's abruptly shifting positions as the shutdown has dragged on. That, in turn, could prompt him to sign bills that restore funding to agencies that have been affected by the shutdown.