Moderate Democrats who have expressed their reservations with the broad strokes, including Sen. Mary Landrieu of Louisiana, Sen. Blanche Lincoln of Arkansas and Sen. Ben Nelson of Nebraska, also met with Reid.
Reid, who has been working to get moderate Democrats on board his plan, will need all party members to support the bill if he wants to break the first Republican attempt at a filibuster, expected to be on Saturday.
The cloture vote on whether to even start debating the bill will be the first test of the support for Reid's health care bill.
Nelson has been one of the biggest question marks for Democrats on health care and, while still undecided, he seemed inclined today to bring a Democratic bill to the floor later this week.
CBO's figures come after weeks of silence from the Senate on the health care debate. The non-partisan group had been working on Reid's proposal since Oct. 26 and, aside from the detail that his bill includes a public option, he had been otherwise mum on the proposals in the legislation.
Reid, on Tuesday, expressed cautious optimism about whether he will get the 60 votes needed to bypass the first of several Republican roadblocks and start debate on health care legislation.
Even as Democrats trudge along with their health care overhaul plan, skepticism amid the U.S. public abounds.
Forty-eight percent of respondents to an ABC News/Washington Post poll released Tuesday said they were in favor of health care overhaul, with 49 percent opposed.
Fifty-four percent of insured Americans said it will increase their own costs. Among all respondents, 56 percent thought it will raise overall costs, six in 10 thought it could shut down many private insurers and 61 percent opposed covering abortions in federally supported plans.
House Democrats narrowly passed their version of health care legislation Nov. 8. Only one Republican joined in the vote and the minority party was nearly unanimous in its opposition. Even 39 Democrats opposed the bill, which would cost $1.2 trillion in the next 10 years.
Democrats are deeply divided on the issue of abortion. Some voted against the House bill because it contained an amendment by Rep. Bart Stupak, D-Mich., that would not only cut federal funding for abortion-related activities, it would also limit access to abortions for people who would receive federal subsidies and would have to buy insurance through a health insurance exchange.
Some Democratic senators, such as Nelson, have said they want to see a similar proposal in their bill.
But other Democrats are outraged that this health care bill is focusing on abortion.
"What happened is after the Stupak amendment passed, people really realized it was an unprecedented restriction on a woman's right to choose," Rep. Diana DeGette, D-Colo., said on "Top Line" Tuesday. "So now everybody's sort of taking a deep breath and saying, 'You know, we really don't want to stop people from buying full reproductive care with their own private money.' I think he won't have the votes when people explain to ... those members exactly what the Stupak amendment does."
Stupak disagreed, saying he has ample support for the amendment.
"They're not going to take it out," Stupak said Tuesday on Fox News. "If they do, health care will not move forward. As we expand health care and the federal role in the health care, that prohibition should apply."