Initial maneuvering on the Senate floor was expected later in the week on the measure, bitterly opposed by Republicans eager to deny President Barack Obama a victory on his top domestic priority.
Officials have said the measure would require most Americans to carry health insurance and would mandate large companies to provide coverage to their workers, as well as ban insurance company practices such as denying coverage on the basis of pre-existing medical conditions.
As rank-and-file Democrats gathered to learn details of the measure, a senior Democratic leadership aide said the Congressional Budget Office had estimated it would spread coverage to 31 million Americans who currently lack it while still reducing federal deficits by a total of $127 billion over 10 years.
The aide also cited a CBO estimate that the bill would achieve cuts of $1 trillion over a decade in projected health care costs. The estimate of 94 percent coverage was less than the 96 percent estimated for legislation the House passed earlier this month, but no precise comparisons were possible without as-yet-unreleased CBO documentation.
The aide spoke on condition of anonymity, saying rank-and-file senators had not yet learned of the details.
Aides have said previously much of the bill would be financed by cuts in projected Medicare payments. Reid has also had under consideration higher payroll taxes for upper wage earners, but there was no word on whether he had decided to incorporate that provision into the measure he crafted.
At its core, the bill would set up new insurance marketplaces - called exchanges - primarily for those who now have a hard time getting or keeping coverage. Subsidies would be available to help defray the cost of coverage for people with lower incomes.
Reid announced two weeks ago it would also include an option for consumers to purchase government-sold insurance, with states permitted to drop out of the system.
Senators emerging from their closed-door meeting with Reid provided further details of the bill.
Sen. Kent Conrad, D-N.D., said the legislation would impose a higher payroll tax on families earning more than $250,000 a year. Sen. John Kerry, D-Mass., said all consumers who purchase insurance from private companies in the exchange would have access to abortion coverage.
He said plans without abortion coverage also would have to be sold, giving consumers a choice. That is less restrictive than a provision in the House-passed bill that has angered liberals and abortion rights supporters.
In a sign of the challenge confronting Reid, the Nevada Democrat met earlier in the day with Sens. Ben Nelson of Nebraska, Mary Landrieu of Louisiana and Blanche Lincoln of Arkansas, moderates within his party who have expressed reservations about the bill.
"He is walking through the particulars with them," said Reid's spokesman, Jim Manley. "We need 60 votes to get this bill to the floor."
Nelson later issued a statement strongly suggesting he would vote with fellow Democrats on an initial showdown expected within days. Landrieu said, "I'm not going to be for anything that doesn't drive down costs over time."
Lincoln, the only one of the three who faces re-election next year, told reporters, "We'll wait and see."
With the support of two independents, Democrats have 60 seats, the precise number needed to choke off any Republican delaying tactics. None of the 40 Republicans is expected to defect on the first test vote, expected by weekend.
Ahead lie weeks - if not more - of unpredictable maneuvering on the Senate floor, where Reid and his allies will seek to incorporate changes sought by Democrats and repel attempts by Republicans to defeat the legislation and inflict a significant political defeat on the president.
Reid was releasing his legislation more than a week after the House approved its version of the health care bill on a near party-line vote of 220-215.
According to estimates from the Congressional Budget Office, that House bill, with a price tag of about $1.2 trillion, would result in coverage for tens of millions of uninsured, and provide 96 percent of the eligible population with insurance.
Two Senate committees approved different versions of a health care bill earlier in the year, and while Reid has said he would produce a blend of the two proposals, in fact he had a virtual free hand to come up with a plan that could command the 60 votes needed to pass.
Anticipating a major struggle, the White House deputized Interior Secretary Ken Salazar and former Senate Majority Leader Tom Daschle to join Vice President Joe Biden in trying to clear the way for the bill's approval over the next several weeks.
Salazar, a former Colorado senator, is viewed as a bridge to moderate Democrats who are far outnumbered by liberals inside the Democratic caucus.
Daschle was Obama's first choice for secretary of health and human services, a position from which he was to try and oversee the administration's drive to enact health care legislation. He withdrew his nomination when it was disclosed he had not paid more than $120,000 in federal taxes over several years.