Democrats expect a Congressional Budget Office (CBO) score of their latest healthcare proposals today or tomorrow, a top House chairman said Wednesday.

Rep. George Miller (D-Calif.), the chairman of the House Education and Labor Committee, said that the majority is hoping to receive the final numbers on their health reform proposals soon, which would enable the legislation to move forward.

"I think we get a report back from the Congressional Budget Office today or tomorrow, and then we'll know the last few changes that need to be made to take it to the House and the Senate," Miller said during an appearance on CNBC.

But Miller, echoing other House Democratic leaders, pressed back against a White House deadline for the House to pass the Senate's healthcare bill before March 18th, when President Barack Obama leaves on an international trip.

"I don't know that it'll be by March 18th," Miller said.

Nonetheless, the veteran lawmaker, an ally of House Speaker Nancy Pelosi (D-Calf.), said there had been productive meetings and that Democrats are moving toward getting the votes they need to proceed on the bill.

"We had a very good session between the House and Senate leadership last night," he said. "I think we can see the votes from here."