Democrats are "arriving at a consensus" over what healthcare reform legislation will look like, a key House committee chairman said Wednesday.

Rep. George Miller (D-Calif.), the chairman of the House Education and Labor Committee, said that Democratic leaders have been meeting with various caucuses over the progress on health reform, and are now "very close" to having finalized a deal.

"We're very close to being there," Miller said during an interview on CNBC. "In the House, we've been meeting with our members on a daily basis. We've met with all the different caucuses -- the Blue Dogs, the New Dems, the Progressive Caucus -- and I think we're arriving at a consensus of the bill we'll bring to the floor."

Fractures had emerged within the House Democratic Caucus in recent months, particularly as liberal Democrats demanded the inclusion of the public (or "government-run") option, while more centrist, Blue Dog members seemed reluctant to back the key provision.

Miller, whose committee was one of three in the House to mark-up its version of the health reform bill, said the process has been "a problem," but also "part of a very healthy debate."

"This Democratic caucus, as diverse as it is...they're committed to passing a bill," he said.