Washington (CNN) -- Health care reform advocates inched closer to victory Wednesday as a high-profile liberal Democrat switched his position and announced his intention to vote for a sweeping $875 billion plan under consideration in the House of Representatives.

Rep. Dennis Kucinich, D-Ohio, said he believes "health care is a civil right." He had previously characterized the bill, which cleared the Senate in December, as little more than a boondoggle for private insurers.

Kucinich was publicly lobbied for his vote by President Barack Obama during the president's visit this week to Kucinich's congressional district in Ohio. He told reporters he's had four meetings with Obama to discuss the bill.

"The president's visit to my district ... underscored the urgency of this vote," Kucinich said. "I have doubts about the bill ... [but] I've decided to cast a vote in favor of the legislation."

He said he ultimately had "to make a decision on the bill as it is, not on the bill as I'd like to see it." Kucinich is a backer of a single-payer health care system under which the government would fund all costs billed by doctors and hospitals.

Kucinich's decision to change his vote is "a good sign," Obama told reporters in the Oval Office. "I told him thank you."

House Speaker Nancy Pelosi, D-California, said she thought Kucinich's switch would make a difference with a large number of liberal activists.

"He's been a supporter of health care for all Americans for a long time," she said. "He has a constituency, and many of those people still don't understand why there isn't a public [option]."

Pelosi has repeatedly expressed confidence that she will have enough support to pass the bill when it comes to the floor for a final vote.

Read more about how votes are lining up

Maryland Rep. Steny Hoyer, the No. 2 House Democrat, indicated Wednesday the vote could come at some point this weekend. He said the leadership is still waiting for final cost estimates from the nonpartisan Congressional Budget Office on a package of changes to the measure.

Asked if the release of the CBO numbers was imminent, Pelosi said, "I would have said ... half an hour ago, hopefully any minute. I think it's going to take a little more time."

She said she had no explanation for the delay.

"I don't know the calculation," she said. "I don't know how they do it. Whatever it is, they're the gospel and we have to live by it."

Later, Pelosi spokesman Nadeam Elshami said that the CBO estimates would not be released Wednesday night. Since the Democrats have said the bill will be available for reading for 72 hours before a vote, the vote can take place no sooner than Sunday, provided the CBO numbers are posted Thursday.

Pelosi needs 216 votes from her 253-member caucus to pass the Senate bill. No Republicans are expected to back it.

A number of House Democrats have refused to state their voting intentions publicly. Twenty-seven House Democrats, however, have indicated they will join Republicans in opposing the Senate plan. That puts opponents of reform 11 votes shy of the 216 needed to prevent Obama from scoring a major victory on his top domestic priority.

Meanwhile, GOP leaders continued to pound away at the legislation on Wednesday, slamming House Democratic leaders for considering the use of a controversial legislative maneuver to pass the Senate bill.

Pelosi may try to help House Democrats unhappy with the Senate bill by allowing them to avoid a direct vote on the measure. She is considering pushing for a vote on a rule that would simply "deem" the Senate bill to be passed.

The House then would proceed to a separate vote on the more popular package of changes to the Senate plan.

"I've never seen anything like the plan that House Democrats hatched this week to jam their health care bill through Congress," Senate Minority Leader Mitch McConnell, R-Kentucky, said Wednesday.

"Historians will remember this as a new low in this debate, the week that America was introduced to the 'scheme and deem' approach to legislating. They'll remember this as the week that Congress tried to pull the wool over the eyes of the public in order to get around their will."

House Minority Leader John Boehner, R-Ohio, said Tuesday that Republicans will try to block the procedure. They will try to force a vote on a resolution requiring the Senate health care bill to be brought to an up-or-down vote.

Boehner has called the maneuver -- also known as a "self-executing rule" -- the "ultimate in Washington power grabs."

House Republicans sent a letter to the Democratic head of the House Rules Committee on Wednesday asking her to move an upcoming hearing on the health care bill to a larger room to account for overwhelming public interest in the issue.

The committee is responsible for deciding whether the full House will have a chance to pass the Senate bill using the self-executing rule.

"While C-SPAN may decide to cover the hearing, that does not satisfy the need for the maximum amount of transparency and openness needed to give the American people faith in this process," the letter said.

"By moving the hearing to a larger room, we can ensure more Americans will have the opportunity to participate in our proceedings and not be turned away at the door."

Where does health care reform stand?

If enacted, the Democratic reform proposal would constitute the biggest expansion of federal health care guarantees since the enactment of Medicare and Medicaid more than four decades ago. The plan is expected to extend insurance coverage to more than 30 million Americans.

The Senate bill also would reduce federal deficits by about $118 billion over 10 years, according to CBO estimates.

Top Republicans contend the plan amounts to an ill-conceived government takeover of the country's health care system. They have said it would do little to slow spiraling medical costs. They also argue it would lead to higher premiums and taxes for middle-class families while resulting in deep Medicare cuts.

Public opinion polls indicate a majority of Americans have turned against the administration's health care reform plan, though individual elements of the proposal remain widely popular.

CNN's Dan Lothian, Charles Riley, Alan Silverleib, Jeff Simon, Deirdre Walsh and Robert Yoon contributed to this report.