Originally Published: 19 APR 23 08:57 ET

Updated: 20 APR 23 08:52 ET

By Annie Grayer, CNN

(CNN) -- House Republicans are trying to restart momentum on a border security package that faced early opposition in the current Congress by beginning to move a slightly revamped package through the committee process on Wednesday, but early reactions indicate many of the same sticking points and hurdles remain.

The conference, which has lambasted the Biden administration over border policy, had hoped to pass a narrow border security bill within the first two weeks of their new majority but blowback from moderates that forced lawmakers back to the negotiating table revealed that delivering on this campaign promise would be much harder than first imagined.

Two Texas lawmakers, Reps. Tony Gonzales and Chip Roy, have staked out opposing positions on how their party should approach border security, particularly when it comes to the issue of asylum -- at times leading to issues between them.

One Republican lawmaker, granted anonymity to speak freely, described the dynamics between the two Texans as "tense" and "personal."

Just last month, Gonzales led a whipping effort on the House floor to sink an amendment from Roy on a different topic because he thought Roy's amendment, which ultimately failed, "was not a good amendment." Roy took to the House floor the day his amendment failed to claim the efforts to sink it were done "for petty, personal reasons."

While border package negotiations were still ongoing, Gonzales previously told CNN, "You're never going to out-border me," while Roy previously said, "I'm not really worried about what [Gonzales] has to say."

Ahead of Wednesday's markup in the House Judiciary Committee however, both downplayed tensions in conversations with CNN and even said they spoke on Tuesday.

"Everyone thinks there is beef between me and Chip," Gonzales told CNN. "There isn't. We have different ideas, different philosophies on it. But him and I are neighbors, we're cordial."

Roy told CNN, "I'm not going to talk about private meetings. Tony and I have had a lot of conversations over time."

Republicans passed their border package out of committee late Wednesday night after many hours of debate. GOP Rep. Thomas Massie joined Democrats in voting against the it.

Behind the scenes, House Speaker Kevin McCarthy and his leadership team have been leading negotiations to try to smooth over sticking points. House Judiciary Chair Jim Jordan, GOP Rep. Mario Díaz-Balart of Florida, who has been representing moderate Republicans, Roy and other leadership allies have been meeting regularly on the package, sources told CNN. The deliberations have ebbed and flowed leading up to the Wednesday markup. As negotiations unfolded, a markup was almost scheduled last month, sources told CNN, but negotiators ultimately wanted more time to continue deliberations.

The new package, as the result of the negotiations, combines eight border bills into one, and while it does not include verbatim Roy's legislation that sparked the initial controversy over asylum, it adopts its essence by largely choking off asylum at the US-Mexico border which is currently permitted under US law.

The package also calls for reinstating the Trump-era "remain in Mexico" policy, which required migrants to stay in Mexico while they awaited their immigration proceedings in the US, marking an unprecedented departure from protocol. That provision, though, would require buy-in from Mexico.

Gonzales, who has pledged to vote against the GOP debt limit plan if the border bill as it stands is brought to the House floor, was quick to say he thinks "a lot" of changes need to be made to the package being circulated.

"It's not just me. I think there's a lot of members that have a lot of issues," he said.

As he walked into McCarthy's office on Tuesday, Díaz-Balart said: "We're still working through it."

GOP Rep. Carlos Gimenez of Florida, without specifying specifically how he would vote, said at a press conference hosted by the Congressional Hispanic Conference with a number of lawmakers to voice concerns over the legislation that he "will never support anything that does not allow for valid asylum claims. That's what America is all about."

Even though border security has broad support among the GOP base, House Republicans are struggling to navigate the challenges of governing in a razor-thin majority even on bills -- like this one -- that are dead on arrival in the Senate, and have resisted committing to when or how the package would pass.

The package will move through the House Judiciary panel, where Roy and a number of other hardline conservatives sit, instead of the House Homeland Security Committee, where Gonzales and Gimenez are members. House Homeland Security Republicans are expected to move a separate border security package through their committee as well.

Asked whether he thinks the package has the ability to pass the House, Jordan told CNN, "I think leaders have committed to putting an immigration bill on the floor. I think maybe there ought to be some tweaks, but we will see. We are working on all of that."

South Carolina Republican Rep. Russell Fry, who serves on the Judiciary panel, told CNN, "We ran on this as part of our commitment to America. And so, we're going to deliver on that for the American people."

The top Democrat on the Judiciary panel, Rep. Jerry Nadler, nodded to the internal GOP infighting over the border security package that has held up legislative action during Wednesday's markup.

"After 3 and a half months of Republican infighting and chaos, the Judiciary Committee is finally holding its first markup of legislation this Congress," Nadler said. "These Republican bills are so extreme that they are opposed by many of their own members."

Some Republicans were quick to dismiss the holdouts.

Rep. Troy Nehls told CNN, "We can still get to 218 without Tony Gonzales."

"(Gonzales) has more areas of the border than any other member in Congress. I'm not going to sit and beat up on Tony Gonzales. But he seems right now to be out on an island by himself right now, as it relates to the Texas delegation," the Texas congressman added.

Roy, meanwhile, framed the opposition to the package as rhetoric "without a whole lot of substance."

"Everybody in the conference supports making sure that an individual who has a legitimate asylum claim can get it heard and get it processed. Nobody disagrees with that. However, the question is how you do that," he said.

Others argued still that the border package did not go far enough.

House Homeland Security Chairman Mark Green, who is expected to release a border proposal of his own and said he is in regular communication with Jordan, told CNN "they're probably having to compromise a little too much for me" on the package being marked up by the Judiciary panel. "We'd like to see it be a little tighter but we also want it to pass."

On the differences of opinion within his party on this issue, Florida Rep. Brian Mast said: "This is Washington, DC, and everybody has different opinions."