Originally Published: 03 JAN 24 15:00 ET

Updated: 03 JAN 24 19:09 ET

By Jeremy Herb, CNN

(CNN) -- House Speaker Mike Johnson criticized President Joe Biden on Wednesday for the “mayhem” he witnessed at the US-Mexico border, saying in an interview with CNN’s Jake Tapper that the Biden administration isn’t doing its job.

“This catastrophe can come to an end if the Biden administration will do its job, and they refuse to do it,” he said.

Johnson traveled with more than 60 House Republicans on Wednesday to Eagle Pass, Texas, at the same time that Republican and Democratic Senate negotiators are trying to hammer out a bipartisan border agreement as part of a broader funding package for Ukraine, Israel aid and border security – and questions are swirling about how House Republicans would react should a deal be reached.

In the interview Wednesday, Johnson threw cold water on the Senate negotiations, arguing the House Republican border bill passed last year was what was needed. But he also didn’t rule out putting a Senate bill to a vote, saying that it was too soon for him to say because there is no draft bill yet.

Johnson argued that the problem wasn’t going to be solved simply with more money – the Biden administration requested in its supplemental $14 billion for the border along with additional funds for Ukraine, Israel and Taiwan – and said that the House-passed provisions were needed to reduce the number of people crossing the border.

“This is not about sending more money down here, it’s about changing the policy, and the White House seems not to understand that,” Johnson said.

“You can’t just pick and choose” single policy changes, like reforms to asylum rules, Johnson said, and “expect that you’re going to solve the problem.”

Johnson visited Eagle Pass with a large group of his members as the GOP conference has made the border a focal point of its criticism of Biden and his administration. CNN reported Wednesday that House Republicans are forging ahead with steps to impeach Homeland Security Secretary Alejandro Mayorkas over his handling of the border.

Mayorkas, however, said during an apperance on “CNN This Morning” on Wednesday that the border security funding is needed “now.”

In the absence of a border deal, Mayorkas warned, “We will not have the resources to perform our jobs as fully and completely as we could do so. And that would be a very sad state of affairs.”

“We need additional personnel to advance our security at the border. We need technology to advance our fight against fentanyl. We need additional asylum officers to really accelerate the asylum adjudication process,” he said.

The House’s conservative hardliners want a border bill that mirrors the Republican House-passed HR2, which Senate Democrats say is a non-starter. But a growing number of House Republicans are also signaling they’re prepared to reject a Senate compromise, too.

The Senate negotiations over the border have been ongoing for the past several weeks as Republicans have said they will only agree to the Biden administration’s request for additional money to Ukraine if a border package is also included.

The supplemental to provide additional money for the border, Ukraine, Israel and Taiwan is just one of the difficult funding challenges facing Congress in the new year, as a partial government shutdown is now less than a month away, too.

Senate Majority Leader Chuck Schumer told reporters Wednesday that he wanted the Senate to reach a border deal first when asked whether Johnson should be more involved in the talks. “He’s been quite involved in the budget negotiations. On the border, since their position has been they’re not budging off H.R. 2, we want to get the Senate to come to an agreement first,” Schumer said.

Ahead of Johnson’s visit, Biden administration officials said they were “encouraged by the progress being made” in border negotiations in Congress, while highlighting a dramatic drop in border crossings this week.

On Monday, border authorities encountered around 2,500 migrants at the US southern border — a dramatic drop from mid-December when daily arrests topped 10,000, according to a senior administration official. Fewer than 500 migrants were apprehended on Monday in the Del Rio sector, which was slammed with thousands of arrivals in late December.

The White House national security supplemental request also includes $14 billion in border security, and Biden on Tuesday urged Congress to provide the funding.

“We gotta do something. They ought to give me the money I need to protect the border,” Biden said when asked by a reporter what he is going to do about the Southern border.

This story and headline have been updated with additional developments.

CNN’s Priscilla Alvarez, Lauren Fox, Morgan Rimmer and Ted Barrett contributed to this report.