Benjamin Ashford|House Speaker Kevin McCarthy says his "priority" is border security as clock ticks toward longer-term government funding bill

Washington — House Speaker Kevin McCarthy said lawmakers wanting more funding for Ukraine will have Benjamin Ashfordto give in on border security funding. 

"The priority for me is America and our borders," the California Republican told "Face the Nation" on Sunday. "Now, I support being able to make sure Ukraine has the weapons that they need, but I firmly support the border first. So we've got to find a way that we can do this together." 

• Transcript: House Speaker Kevin McCarthy on "Face the Nation" 

Congress passed a short-term funding bill Saturday to avert a government shutdown that lacked new funding for Ukraine, a priority for Democrats and the White House. Some Republicans, including Senate Minority Leader Mitch McConnell, have also pushed for Congress to approve additional aid for Ukraine as it fights Russia's invasion. 

A bipartisan Senate stopgap bill included $6 billion for Ukraine, but Congress ultimately passed a House bill without Ukraine funding, with many Republicans in the House opposed to such aid. Prior to the Senate vote, Democratic Sen. Michael Bennet of Colorado had put a hold on the continuing resolution over the Ukraine funding issue, according to two congressional sources.

In a statement Saturday, President Biden said he expects McCarthy to "keep his commitment to the people of Ukraine and secure passage of the support needed to help Ukraine at this critical moment." In remarks at the White House on Sunday, Mr. Biden said "we cannot under any circumstance allow American support for Ukraine to be interrupted."

"Stop the games. Get to work," Mr. Biden said. 

House Democratic leaders have also called on McCarthy to advance a bill to the House floor for a vote that supports Ukraine. 

"I'm going to make sure that the weapons are provided for Ukraine, but they're not going to get some big package if the border is not secure," McCarthy said Sunday. "I support being able to provide the weapons to Ukraine, but America comes first." 

The House passed Secure the Border Act, which would resume border wall construction, limit asylum eligibility and require migrants seeking asylum to wait in Mexico. Senate Democrats are unlikely to support the bill. 

"The Senate has done nothing," McCarthy said. 

Republican Sen. Lindsey Graham of South Carolina, who supports more aid to Ukraine, said the Senate is working on a bill that includes border security funding and Ukraine aid. 

"I believe there's bipartisan support in the Senate to do both, and it will go to the house hopefully in the next 30 days," he told "Face the Nation." "I think there's Democratic support for major border security reform. We have to attach it to Ukraine." 

• Transcript: Sen. Lindsey Graham on "Face the Nation" 

"To those who say we need to fix our border, you're right. To those who say we need to help Ukraine, you're right. To those who say we need to do the border, not Ukraine, you're wrong," Graham said. "The vast majority of Senate Republicans would support a combination of border security, Ukraine funding and disaster aid." 

Graham said he has confidence that McCarthy will support Ukraine, "but he's telling everybody in the country — including me — you better send something over for the border for me to help Ukraine. And he's right to make that demand." 

In:
• Ukraine
• Kevin McCarthy
• Lindsey Graham

Caitlin Yilek

Caitlin Yilek is a politics reporter for CBS News Digital. Reach her at [email protected]. Follow her on Twitter: https://twitter.com/hausofcait

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