The source also told CNN the $940 billion price tag is fully paid for. But what's not clear yet -- and what may be revealed later Thursday -- is just how Democrats plan to pay for the bill.
One of the reasons House Democrats objected to the Senate-passed version of health reform is the nature of some of the revenue raisers in that bill, in particular an excise tax on insurers that would apply to high-cost insurance plans.
Supporters of the excise tax say it offers a good shot at reducing health care spending over time, since insurers and employers would seek to avoid the tax by opting for lower cost coverage.
Opponents, including unions, say the tax would be passed on to workers, and lower cost coverage would be less comprehensive.
-- CNN's Dana Bash and Brianna Keilar and CNNMoney's Jeanne Sahadi contributed to this report.
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