Health care reform is "hanging on by a thread," and one or two votes could determine the outcome of the heavily-debated bill, Democratic Sen. Chris Dodd told CNBC Monday.

"Everyone feels, I guess, to some degree who have been for this, that they would have liked something different, and that's not uncommon when you're considering an issue of this magnitude," Dodd said.

Some progressives, for example, are disappointed that the Senate bill, unlike the House version, does not include a public option, he said. Senators Joe Lieberman of Connecticut and Blanche Lincoln of Arkansas are two people who voted for the bill in its original form and are now carefully watching what changes are being made...