Senate leaders 'encouraged' by border negotiations as aid discussions grind on

Senate Republican Leader Mitch McConnell said Monday that he's "encouraged" by ongoing border negotiations among senators and White House representatives, but that there remains a "significant number" of issues that still need to be worked through before brokering a deal on President Joe Biden's aid package for Ukraine and Israel.

"Addressing the border crisis at home is a fundamental part of legislation that will help America meet each of the most glaring national security challenges we face around the world -- and there are a number of significant issues our colleagues are still working to resolve," McConnell said on the Senate floor Monday afternoon.

With the Senate's holiday recess delayed, McConnell made clear that his conference will not be rushed into considering a bill on a more expedited timetable than they'd like. Last week, Majority Leader Chuck Schumer said the Senate would stay in Washington and vote on the national security aid package some time this week.

Many Republicans are trying to push consideration of the supplemental aid package, which is expected to include aid to Ukraine, Israel, Taiwan and border policy provisions, into the new year.

"The effects of years of failed border enforcement are compounded: border security policy is complex, and our colleagues at the negotiating table are clear-eyed about the fact that getting this agreement right and producing legislative text is going to require some time," McConnell said. "Senate Republicans will not make up for others showing up late to the table by waiving our responsibility to carefully negotiate and review any agreement before voting on it."

As it currently stands, negotiators have not yet reached an agreement in principle on border policies. Even if they do so this week, the likelihood that it could be turned into text with enough time to allow Republicans the time to consider it is extremely low.

In is own floor remarks Monday afternoon, Schumer said border negotiators made progress toward a deal, but conceded that negotiations are not yet complete.

"Over the past week, Democrats and Republicans have made important progress towards an agreement on the national security supplemental. While the job is not finished I am confident we're headed in the right direction," Schumer said.

Schumer said he was encouraged by "significant progress," but acknowledged that legislating around the border is "among the most difficult things we've done in recent memory."

He also said that he knows negotiations may continue to take time.

"Everyone knows that something should be done to fix our broken immigration system, but we can't do so by compromising our values. Finding the middle ground is exceptionally hard, and both sides must accept that they will have to make concessions. And it's going to take some more time to get it done," Schumer said.

The Biden administration's pitch is drawing the ire of the Congressional Hispanic Caucus as concerns grow that the White House will allow major border concessions in a push to get the aid deal through.

Several members of the caucus issued a statement last week urging Biden to reject "Trump-era immigration policies being considered in the ongoing negotiations around the supplemental aid package."

"It is unconscionable that the President would consider going back on his word to enact what amounts to a ban on asylum," Congressional Hispanic Caucus Chair Rep. Nanette Barragan and Sen. Alex Padilla -- both California Democrats -- wrote in a joint statement.

Rep. Delia Ramirez, D-Ill., said she is "disappointed" members of the Congressional Hispanic Caucus have not been part of the negotiations even though they are "the ones that understand immigration policy the best," she said on CNN over the weekend.

"This is what I've worked on for my entire life," Ramirez said of immigration policy. "And for the fact that there are conversations between some senators -- none of them that understand or have lived or experienced that. I just came from Guatemala on a committee delegation trip -- and Honduras -- talking to migrants. And we have not been in the room, yet decisions that are going to impact our community severely are being negotiated without us being in the room."

It is not yet clear whether Schumer will attempt to hold a procedural vote on the yet-to-be drafted bill this week. But Republicans have said they'd block any effort to move forward without bill text.

"I'm encouraged by our colleagues commitment to keep making steady progress in their negotiations over the coming week and beyond," McConnell said.

Still, there is no clear timeline for where things are headed.

ABC News' Sarah Beth Hensley contributed to this report.