• House Speaker Kevin McCarthy, R-Calif., told CNBC's "Squawk Box" that the current Senate bill "does nothing to deal with the border security."
• The Senate earlier this week introduced a bill that would keep the government open through Nov. 17, giving lawmakers more time to reach a deal on a larger budget plan.
• Even still, McCarthy said he's hopeful a deal will be reached.

House Speaker Kevin McCarthy, R-Calif., on Thursday criticized a short-term Senate government funding bill — stoking more fears that a shutdown could take place — saying the measure would not bolster border security.

"I look at the current Senate bill that does nothing to deal with the border security. Don't take my word for it. The governor of Massachusetts declared a state of emergency," he told CNBC's "Squawk Box," while also noting New York City's increased spending on shelter for migrants.

"This is something that Democrats and Republicans want to have done," he said.

The Senate earlier this week introduced a bill that would keep the government open through Nov. 17, giving lawmakers more time to reach a deal on a larger budget plan.

McCarthy's comments came as lawmakers race to reach an agreement on a government funding plan before a deadline this weekend. If a deal isn't reached by then, the government would shut down, sending ripples through the U.S. economy and capital markets.

McCarthy also said he's facing challenges from House members within his own party as the negotiations continue.

"I've got members who have held us up since the summer not to be able to bring our appropriation bills up. Otherwise, we probably have them all done," he said. "I've got members who will not vote to have a stopgap measure to continue to fund government. I got members who say they'll never vote for it."

Even still, McCarthy said he's hopeful a deal will be reached.

"At the end of the day, we will get this done."