McConnell said Sunday that a CHIP extension and disaster aid would be addressed in a spending bill before December 22, but not immigration.
House Minority Leader Nancy Pelosi and Senate Minority Leader Charles Schumer said they've agreed to meet on Thursday with President Donald Trump and Republican Congressional leaders to discuss a year-end spending deal as a possible government shutdown looms as early as Saturday.
A vote in the House is expected as soon as Wednesday on the measure.
In the Senate, Majority Leader Mitch McConnell, R-Ky., said his preference is for a two-week funding bill.
House Armed Services Committee Chairman Mac Thornberry (R-TX) told Inside Defense over the weekend he supports the two-week CR extension, provided he is promised a fiscal year 2018 defense spending increase.
Senate Republicans and Democrats today voiced their support for a brief extension to a stopgap continuing resolution that would prevent a federal government shutdown Friday.
"Problem is they want illegal immigrants flooding into our Country unchecked, are weak on Crime and want to substantially RAISE Taxes", Trump's tweet said.
The Democrats tweeted their hope that the president will "go into this meeting with an open mind, rather than deciding that an agreement can't be reached beforehand". He said Democrats had offered in return to toughen border security, a Republican priority.
"As negotiations with our Republican counterparts continue, we are hopeful the president will be open to an agreement to address the urgent needs of the American people and keep government open", Pelosi and Schumer wrote.
In further indication of the problems GOP leaders face, 34 House Republicans sent a letter to House Speaker Paul Ryan, R-Wis., urging him to hold a vote by year's end on extending protections for hundreds of thousands of immigrants who arrived in the US illegally as children.
"We have to provide funding for community health centres and (the Children´s Health Insurance Program), as well as relief for the millions of Americans still reeling from natural disasters", they added.
He noted that he does not think the federal government would shut down over Congress' failure to address the issue over the Deferred Action for Childhood Arrivals program since lawmakers have until March to come up with a plan to address DACA.
Getting an immigration deal enacted in December would cause an eruption in House GOP ranks, where many conservatives oppose the idea. There are also demands for money for battling opioid abuse.
Monday, the meeting was put back on the schedule for Thursday.
A key House Republican leader acknowledges that some tax cuts in the sweeping tax legislation must expire to comply with Senate budget rules. Democrats would likely win less for nondefense agencies.
Democratic votes will definitely be crucial in the Senate, where Republicans by themselves lack the 60 votes needed to approve the legislation.
GOP leaders hope to send Trump a final tax package before Christmas, and there's a growing consensus that they have a strong chance to succeed. They have modest differences over items like whether to reduce or fully repeal the tax on the most expensive estates.
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