Just 14 Republicans joined all voting Democrats in Tuesday's futile effort to void Trump's declaration of a national emergency at the Southwest border.
The final vote was 248 yeas to 181 nays.
House Judiciary Committee Chairman Jerrold Nadler said he supported the Republican effort because he wants to know "what prompted such alarm" among officials.
By invoking that power, Trump has said he will shift $3.6 billion from military construction to erecting barriers along that boundary.
The House approved the resolution blocking Trump's emergency by 245-182 in February. "Today's vote simply reaffirms Congressional Democrats are the party of Open Borders, Drugs and Crime!"
Trump vetoed that measure nearly immediately.
If the House vote fails, the Senate won't attempt its own override and the veto will stand.
When Trump entered the private weekly lunch, Republicans could be heard applauding.
"I think that the president is doing exactly what he should, which is leaving that decision in the hands of the attorney general, and we'll see what decision he makes on that front", White House press secretary Sarah Sanders said Monday on the "Today" show.
Later on Tuesday, Papadopoulos said his attorneys requested a pardon from President Trump and if granted, he would be "honored to accept it".
President Donald Trump says the outcome of special counsel Robert Mueller's report on Russian election interference "could not have been better". Moscow has denied meddling. But right now the Barr letter appears to be more of a political Rorschach test than a game-changer - and Trump's gleeful if inaccurate claims that he's been "fully exonerated" don't seem to be improving his standing with voters.
"Even though the two issues clearly aren't related, it increases the president's strength and popularity and puts him in a stronger position", Republican Representative Tom Cole said before the House vote.
The vote also came on Speaker Nancy Pelosi's birthday.
After Congress signed an appropriations bill earlier this year that only approved $1.4 billion for border security, Trump declared a national emergency to appropriate additional funds to construct his wall along the U.S. -Mexico border. He urged his colleagues to override the veto, arguing that there's a "humanitarian crisis" at the border but "no invasion" that would justify Trump's move.
When asked specifically about accusations of collusion and obstruction of justice, 48 percent of poll respondents said they believed "Trump or someone from his campaign worked with Russian Federation to influence the 2016 election", down 6 percentage points from last week.
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