House Minority Leader Kevin McCarthy said Tuesday the tentative government funding deal shows that Democrats caved on President Donald Trump's demand for a wall along the U.S.-Mexico border. House Speaker Nancy Pelosi's office immediately fired back.

McCarthy said Pelosi had insisted she would provide "'no money for a wall,'" but in the compromise deal "that's not the case."

"The Democrats have now agreed to more than 55 miles of new barrier being built," the California Republican added in an interview on CNBC's "Squawk Box."

In response, Pelosi's deputy chief of staff Drew Hammill told CNBC that "there is no wall money in this agreement" and that "Democrats have supported physical barriers in the past."

"This agreement has the same amount of funding for physical barriers that last year's omnibus had," he added.

Congressional negotiators said they reached a tentative deal late Monday to fund the government and avoid another shutdown. A congressional source told CNBC it would put about $1.4 billion toward physical barriers, but not the concrete wall that the president wants.

It's not known whether Trump will accept the deal. Trump's demand for $5.7 billion to build 215 miles of wall along the southern U.S. border led to a funding stalemate in December and a record 35-day partial government shutdown.

On Jan. 25, the president signed legislation to put federal employees back to work. However, Trump threatened to let funding lapse again or declare a national emergency on illegal immigration if Congress didn't craft a deal he likes.

"The president has a few more tools in his toolbox," said McCarthy, without elaborating on what those tools might be.

The tentative funding agreement would also reduce the cap for Immigration and Customs Enforcement detention beds by about 17 percent from the current 49,057 to 40,520, according to the source.

"The Democrats changed course when they said, 'There would be no detention beds,'" McCarthy said. "They backed away on that. Now we are able to have those detention beds again. It's not as high a number as we would have liked."

A senior Democratic aide told CNBC that Democrats never advocated for "no detention beds," adding the reduction in beds in the tentative deal provides a "critical check on the Trump administration's mass deportation agenda."

The White House was not immediately available to respond to CNBC's request for comment.

—CNBC's Jacob Pramuk contributed to this report.