"I am proud that my colleagues on both sides of the aisle have joined us in overturning this veto so we can get back to the business of governing".
The outcome is highly uncertain heading into the rare holiday-week session. The split comes at a unsafe time politically for the GOP - just a week before two runoff races in Georgia that will determine control of the Senate.
McConnell, who has said little publicly on Trump's request, objected but gave nearly no indication of his plans ahead. "Our leaders (not me, of course!) are pathetic".
Trump claimed on Sunday that he was putting pressure on Congress to remove billions of dollars in "pork" from the bill.
Many of Trump's voters remain loyal to the president, while others share Republicans' concerns.
"I'm delighted to support the president", said Perdue on Fox News. That could include more relief checks.
In his tweets on Tuesday, Trump also lashed out at Republican leaders for failing to support his baseless claims that he won the November 3 election against Democrat Joe Biden. "Let's do our job", he tweeted after the House vote Monday night.
The action came just hours before a government shutdown, and days after the president opposed the bill over "wasteful and unnecessary items".
"Weak and exhausted Republican "leadership" will allow the bad Defense Bill to pass", Trump tweeted.
The House voted 322 to 87 on Monday to override Trump's veto of the $740.5 billion defense bill, with 109 Republicans breaking ranks and siding with the Democrats.
The package totals $2.3 trillion and includes a round of $600 direct payments to Americans suffering from the economic fallout of the coronavirus pandemic and $300 weekly payments of enhanced unemployment benefits-a benefit potentially cut short for one week because of the delay in signing the bill, which passed Congress on December 21 and was presented for his signature a few days after.
The House also voted overwhelmingly to override the President's veto of a defence policy bill. The new Congress is set to be sworn in Sunday. The effort failed because House Minority Leader Kevin McCarthy, a Republican, didn't approve it. The stimulus bill he signed on Sunday will provide most Americans making less than $75,000 a year a $600 check. It extends eviction protections, adding a new rental assistance fund.
However, he called for the payments to be increased to $2,000 to assist Americans hurt by the impact of the coronavirus pandemic on the economy.
Biden spoke to reporters briefly Monday in Wilmington, Del., about other matters, but he was asked as he left the lectern about whether he supported $2,000 direct payments.
The president was prepared to sign the relief bill on Christmas Eve at his resort in Palm Beach, Florida, but he "changed his mind" at the last minute, a source told CNN. Senate Republican leader Mitch McConnell of Kentucky has not indicated that he will bring the matter up for a vote.
The delay meant that millions of Americans temporarily lost unemployment benefits.
McConnell said it was important for Congress to continue its almost six-decade-long streak of passing the defence policy bill.
He added that "more money is coming" and vowed to "never give up" his fight for the American people.
For now, the administration can only begin work sending out the $600 payments.
Trump has offered a series of rationales for rejecting the bill.
Democratic representative Adam Smith, chairman of the House Armed Services Committee, said Trump's veto "made it clear that he does not care about the needs of our military personnel and their families".
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