"This would be beneficial to both taxpayers and homeowners," Cummings said.

But the Maryland lawmaker did admit that DeMarco's resignation could cause additional headaches.

"The problem is, if he steps down, there's three people who come under him, one of them would have to be appointed, unless the president could successfully nominate and confirm his own choice. The Congress — that is, the Senate — doesn't seem willing to do that, so we're kind of stuck between a rock and a hard place," Cummings said.

He also credited DeMarco for working with him on some issues, including allowing mortgage holders to defer payments.

"We've seen him inch toward some of our positions," Cummings said.