"Trump's border wall does nothing to promote San Diego's robust economy and our positive worldwide ties with Mexico", Democratic Council President Pro Tem Barbara Bry said, according to The Washington Free Beacon.
The president's suggestion puts him at odds with members of his own party in Congress, where many Republicans are facing tough re-election fights this November.
At the White House meeting last week, Trump, Ryan and McConnell agreed that Congress is on track to enact more than half of federal spending before the new budget year begins October 1, but that DHS funding, including the border wall money, doesn't have to be settled before then, according to a person familiar with the meeting who was not authorized to discuss it publicly and spoke on condition of anonymity.
"I just want great border security".
Beyond building a wall, the administration also wants to do away with so-called "chain migration" allowing relatives of immigrants to come to the country, and the diversity visa-lottery program, and to move toward what Trump calls a "merit-based" immigration system.
When asked about the meeting, Senate Majority Leader Mitch McConnell, R-Ky., said Tuesday that he and other Republicans support the president's goals as they try to go through a normal appropriations process "that prevents a big event at the end of the fiscal year".
Ryan added that Trump is "willing to be patient to make sure we get what we need so that we can get this done".
"I think the president's very serious about his wanting more money to fund the wall", Shelby said on Tuesday.
Trump has touted his wish for a wall along the US-Mexico border since his campaign, and has previously claimed he would be able to get Mexico to cover the cost.
Rudy Giuliani Says Former Trump Lawyer Michael Cohen's Credibility Is 'Destroyed'
Cohen alleges that he was present, along with several others, when Trump was informed of the Russians' offer by Trump Jr. Sam Nunberg, a former Trump campaign aide, said Sunday on "Meet The Press" that he sided with the Trumps over Cohen.
And that will likely mean far less funding for Trump's proposed border wall than he initially sought, analysts said.
Sen. Susan Collins, R-Maine, said shutdowns represent "a failure to govern effectively".
Trump on Monday said he had no "red line" for precisely what he would require from Congress, and he made no comment on timing.
Trump began his policy of "zero tolerance" this spring, prosecuting all migrants caught entering the USA without authorization. Back in February, Trump said that he'd "love to see a shutdown" if the government did not address border security.
The House is in recess and won't return until after Labor Day.
Trump's tweet on Monday lacked something his post on Sunday had - a threat to shut down the government if he doesn't get his wall. Because Trump's wall was funded during the current fiscal year, it would continue for the length of the extension.
Both Speaker of the House Paul Ryan and McConnell met with Trump last week to discuss funding the government.
The House and Senate have already approved a separate package funding the departments of Energy and Veterans Affairs and are working out differences in the competing versions. They have the strength to derail legislation in the closely divided Senate.
Some 2,500 children were separated from their parents as part of Republican President Donald Trump's "zero tolerance" policy towards illegal immigration.