Democratic Rep. Henry Cuellar (Texas) told "Fox News Sunday" that his party would likely support "some sort of enhanced barrier," but not a "wall."
Cuellar told host Chris Wallace, "First of all, we are not going to have a wall." He also called walls a "14th-century" solution.
"Now, we can look at some sort of enhanced…barrier," Cuellar said. "That's certainly something we can look at. But I have to say living on the border, you have to let the local Border Patrol chief have the say-so, and let the local communities be involved so they can come up with maybe some sort of enhanced barrier. But again, Washington cannot dictate what sort of barrier and where to put it at."
Following a partial shutdown, the federal government was reopened and funded through Feb. 15 in an attempt to allow more time for President Donald Trump and lawmakers to continue negotiations for the proposed wall. Trump wants to build a $5.7 billion wall along the U.S.-Mexico border.
"If we don't get outside pressure, the committee can sit down and work this out," Cuellar said. "…We can work out a deal. I know we can sit down and work it, if we just don't get any outside pressure, do what we need to do, and I feel the process as appropriators, House and Senate Democrats, Republicans; we can work something out."
Sen. John Hoeven (R-N.D.) also told the news program that some sort of "barrier" is needed along the border.
"I think we can get to a solution, but it does need to include barrier funding," Hoeven said. "It needs to include personnel, technology and funding for a border barrier."
Although House Speaker Nancy Pelosi has said there will be no wall, several other prominent Democrats such as House Majority Leader Steny Hoyer (D-Md.) and Rep. Ben McAdams (D-Utah) have "distanced themselves from Pelosi's hardline stance," Fox News reported.
Trump has hinted that he could declare a national emergency if Congress does not agree to fund his proposed wall.
The White House also said it would agree to a "large down payment" on the wall although Pelosi rejected the idea.