Congress and the White House are working on a deal for a two-week extension of government funding that would push the deadline for a fight over a possible government shutdown and money for President Trump's border wall until December 21.
The measure, which includes funding for the Homeland Security and Interior departments and other federal agencies, would push a showdown over funding for a wall on the southern border to December 21.
Even some Republicans balk at spending more than the $1.6 billion for fencing and other security improvements already provided.
Congressman Hice's comment arises as House Minority Whip Steny Hoyer (D-MD) said on Tuesday that Democrats could give President Trump up to $1.6 billion so long as much of the spending goes toward border security, not building the wall.
Trump's plans to build a wall at the US-Mexico border were well publicised throughout his presidential election campaign.
The trouble spot is homeland security, where Mr. Trump has demanded the bill include $5 billion for his U.S. -Mexico border wall.
Conservative Republicans say that with the Democrats taking over the House in January, now could be their last chance to secure border wall money for Mr. Trump. We will close the entire Southern Border if necessary.
Congress is expected to introduce a two-week temporary funding bill to avert a federal government shutdown this week over President Donald Trump's border wall as business in the Capitol comes to a standstill for ceremonies honoring former President George H.W. Bush.
Trump had been expected to meet Tuesday with the two top Democratic leaders on Capitol Hill - House Minority Leader Nancy Pelosi of California and Senate Minority Leader Charles E. Schumer of NY - to discuss how to resolve the remaining sticking points on appropriations, according to sources familiar with the talks. The meeting has been tentatively rescheduled for December 11, said a White House official who was not authorized to speak publicly and spoke on condition of anonymity.
"I would absolutely consider it and probably give it", Trump told reporters.
The Senate, narrowly controlled by Republicans, would also have to approve the measure this week, which would continue funding for several agencies at last year's levels.
Senate Homeland Security Appropriations Chairwoman Shelley Moore Capito said that having the new funding deadline just days before Christmas could increase pressure on lawmakers to come to an agreement.
While Trump has pushed Democrats to build the wall, Schumer and Pelosi face growing pressure from the party's liberal wing to block it.
"I think majority would want to pass our appropriation bills", Shelby said.
Almost three-quarters of the federal government has been funded for the fiscal year that runs through September 30, 2019, but the stalemate remains over wall funding and several remaining federal agencies.
The current deadline is midnight on Friday, Dec. 7.