Department of Homeland Security Secretary Alejandro Mayorkas said Thursday that "Republican and Democratic senators are at the table to discuss how the broken immigration system should be fixed," although he avoided speaking about specifics amid high-stakes negotiations between both parties as another government shutdown looms. 

"This is all about solutions, not making the problem worse by taking away the funding that our public servants rely on to do their work in the service of the American people," Mayorkas told "CBS Mornings."

The White House has asked Congress to provide more funding for Israel and Ukraine, but Republicans are insisting on tying that aid to a border security package. A bipartisan group of senators has been trying to work out a deal, but they are coming up against shutdown deadlines as several key government programs are only funded through Jan. 8, and others through Feb. 2.

Meanwhile, House Republicans, including House Speaker Mike Johnson, have moved a step closer to impeaching Mayorkas, with an initial hearing scheduled for Jan. 10. The House Homeland Security Committee has alleged that Mayorkas has intentionally exacerbated the situation at the border.

Mayorkas did not address those accusations and instead said his focus is on his department and not political rhetoric.

"We are focused here on solutions," said Mayorkas.

Mayorkas said when people come to the United States at the border, they are placed in immigration enforcement proceedings.

"Those proceedings take many years because our system is broken and it is also underfunded. We need Congress to fix the system, and we need the resources to administer it."

There was a record number of attempted border crossings in December, and Border Patrol processed nearly 50,000 migrants who entered the U.S. illegally in just five days. In November, Border Patrol agents apprehended more than 191,000 migrants who crossed the U.S.-Mexico border unlawfully. This month, as many as 10,000 migrants were apprehended daily at the southern border.

Mayorkas pointed to a global migration challenge, not unique to the United States, as a reason for the border crisis.

As more Democratic mayors criticize Texas Gov. Greg Abbott for sending busloads of migrants to the city "without any coordination," Mayorkas said he is working Congress to assist in funding the city resources and help the cities in managing the record number of migrants, but stressed the need for collective efforts to manage the migration challenges.

"Do you think it is responsible governance for one governor to refuse to coordinate, communicate, cooperate with other state officials around the country and just unilaterally bus people to another locality without informing the receiving locality so that we can work together to address a challenge that our country faces? Is that the type of patriotism and governance that we expect of our officials?" said Mayorkas. 

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