Washington (CNN) -- House Republicans moved one step closer Tuesday to fulfilling their 2010 campaign promise to repeal President Barack Obama's controversial health care overhaul.

GOP leaders started a formal debate on a measure to repeal the overhaul, and have scheduled a repeal vote for Wednesday. The new Republican congressional majority, in keeping with its "repeal and replace" mantra, will then instruct various House committees to craft alternatives to the law.

It is time to repeal this "job-stifling, cost-increasing, freedom-limiting law," declared Rep. Lamar Smith, R-Texas.

While the measure is expected to pass the new Republican-led House, it has little chance of clearing the Democratic-controlled Senate or surviving a presidential veto.

Most Republicans have acknowledged the virtual impossibility of an outright repeal, but have indicated there will be attempts to defund portions of the measure or eliminate specific provisions in the months ahead.

Despite the unlikelihood of a successful repeal effort, Obama and top Democrats expressed strong support for the measure Tuesday. Obama said in a statement that the health care law's many benefits needed to be maintained.

"I'm willing and eager to work with both Democrats and Republicans to improve the Affordable Care Act. But we can't go backward," Obama's statement said.

Other Democrats, meanwhile, tore into the Republican effort, warning that a reversal would be catastrophic to small businesses and unfair to millions of Americans depending on the reform to guarantee coverage.

"We will stand firm against any attempts to prevent (people) from having access to quality health care," House Minority Leader Nancy Pelosi, D-California, told CNN's Wolf Blitzer.

The Department of Health and Human Services released an analysis Tuesday morning warning that almost 130 million nonelderly Americans with pre-existing conditions would be at risk of losing their insurance without the guarantees provided by the legislation.

"The new law is already helping to free Americans from the fear that an insurer will drop, limit or cap their coverage when they need it most," Health and Human Services Secretary Kathleen Sebelius said. "Americans living with pre-existing conditions are being freed from discrimination in order to get the health coverage they need."

Karen Mills, the head of the Small Business Administration, told reporters a repeal would result in countless small businesses losing new tax credits that will be provided in exchange for expanded employee coverage.

Undoing Obama's signature domestic reform "will only weaken U.S. businesses and return us to a world of out-of-control costs," said acting Deputy Commerce Secretary Rebecca Blank.

Conservatives insist the reform, as currently written, will hamper prospects for long-term economic growth while doing little to slow spiraling medical costs.

"Repealing the job-crushing health care law is critical to boosting small business job creation and growing the economy," House Speaker John Boehner, R-Ohio, wrote online Monday.

Democrats have pointed out, among other things, the increased number of Americans covered by the law. They've also seized on a recent analysis from the nonpartisan Congressional Budget Office saying that a repeal of the overhaul would add $230 billion to the federal debt by 2021.

Democrats argue that analysis undermines Republicans' emphasis on fiscal responsibility.

GOP leaders, in turn, insist the analysis was based on unrealistic economic and fiscal assumptions originally provided by Democrats. Nonetheless, Republicans have exempted a repeal of the health care law from new rules prohibiting legislation from adding to the federal debt.

The CBO analysis indicates Republicans may have trouble moving ahead with their long-term strategy of defunding the law. The measure includes $106 billion in new spending authorizations that Congress will eventually need to appropriate, according to CBO Director Doug Elmendorf. But $86 billion of those authorizations cover politically sensitive programs that were already in existence before the passage of health care reform.

Certain key provisions -- such as the law's Medicaid expansion and the extension of new insurance subsidies -- cannot be defunded without a direct repeal vote.

Leading members of both parties agree on the need for a limited number of changes to the law. Specifically, they have expressed concern over a rule, scheduled to take effect in 2012, requiring businesses to issue 1099 tax forms to any individual or corporation from which they purchase more than $600 in goods or services in a year.

"A lot of our small businesses came to me (after the health care overhaul passed) and said, 'There's a lot of paperwork I now have to fill out,' " Sen. Kirsten Gillibrand, D-New York, noted Sunday on CBS's "Face the Nation." "We can change that. That's something we can absolutely agree on."

Mills said Tuesday the administration also backs a repeal of the rule.

The health care reform law remains extremely controversial, according to the latest public opinion surveys. While Republicans campaigned last fall on a promise to push for a repeal, a number of Democrats believe they can energize their political base while attracting moderate voters by highlighting the more popular protections that could be lost without the reform.

"The Affordable Care Act gave your family the same health protections members of Congress get," declares a cable television ad released Tuesday by the progressive advocacy group Americans United for Change. "Republicans want to take that protection away from your family."

While the health care debate has often become emotional, leading Republicans and Democrats have promised a more civil discourse in the wake of the January 8 shootings in Arizona. The health care debate during the last Congress was marked by months of acrimonious partisan exchanges, including a series of angry town hall meetings held by congressional Democrats during the summer of 2009. A number of threats were reported and congressional district offices were vandalized at the time.

CNN's Alan Silverleib and Tom Cohen contributed to this report.