WASHINGTON (CNN) -- A preliminary estimate from the Congressional Budget Office projects that the House Democrats' health care plan that includes a public option would cost $871 billion over 10 years, according to two Democratic sources.

CBO also found that the Democrats' bill reduces the deficit in the first 10 years.

This new CBO estimate, which aides caution is not final, is significantly less than the $1.1 trillion price tag of the original House bill that passed out of three committees this summer. More importantly, it comes under the $900 billion cap set by President Obama in his joint address to Congress last month.

CBO analyzed what House Speaker Nancy Pelosi calls a "more robust" public option -- one that ties reimbursement rates for doctors to current Medicare rates, plus a 5 percent increase.

At a meeting with House Democrats on Tuesday night, Pelosi did not release CBO's preliminary numbers, but told members that CBO told leaders the House bill would cost well below $900 billion. Aides say final CBO numbers could be released on Wednesday.

Senior Democratic aides told CNN that House Democratic leaders are likely to put this version of the public option favored by liberal Democrats in the final bill they are drafting. While no final decision has been made, on Tuesday night Speaker Pelosi made the case to House Democrats that this approach saves the most money and would put the House in a better negotiating position when it comes time to negotiate a final health care bill with the Senate.

Pelosi instructed House Democratic Whip Jim Clyburn, D-South Carolina, to begin canvassing all House Democrats on Wednesday to determine whether this bill had enough votes to pass in the House. According to several sources in the meeting, Pelosi acknowledged she did not currently have the 218 votes needed to pass this version on the House floor, but believed she was close to having around 200 votes.

Moderate, "blue dog" Democrats in the House largely oppose the robust public option and instead argue for a government run insurance option that could negotiate reimbursement rates directly with doctors and hospitals. CBO's analysis of that approach was not available according to Democratic sources, but aides say the preliminary analysis shows it does not save as much as the approach pushed by Pelosi.

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