The Democratic-led Senate is likely to ignore the bill, and the White House issued a veto threat in the event it passed.
The House is also expected to vote Wednesday on another bill to block funding for a part of the law that offers grants for school-based health center construction.
Both bills would take away the authority of the secretary of the Health and Human Services, as prescribed in the health care law, to distribute money for the two programs without going through the annual congressional budget process.
"Shockingly, the Congress gave an executive branch official the sole authority to determine the size of the appropriation," said Rep. Fred Upton, R-Mich., chairman of the House Energy and Commerce Committee and sponsor of the health exchange bill. "Without further congressional action, the secretary can literally spend hundreds of billions of dollars" at her own discretion.
The exchanges, said Sen. Tom Harkin, D-Iowa, chairman of the Senate committee that oversees health issues, gives states "new authority and flexibility to serve their citizens' needs. This legislation would roll back those gains and hurt American families. As I've said before, bills to defund the health care law will be dead on arrival in the Senate."
The non-partisan Congressional Budget Office said passage of the Upton bill would reduce the deficit by about $14 billion over the next decade, although the government would then need to go to Congress for the money needed to help states set up the health insurance markets.
The exchanges are a key element in the new health care system envisioned by the law. Starting in 2014, the exchanges will offer one-stop shopping for people and small businesses buying coverage directly from an insurer. Most people buying insurance through the exchanges would be eligible for taxpayer-financed subsidies, and participating plans would have to take all applicants, regardless of prior health problems. Sick people or seniors could not be charged higher premiums.
If a state does not set up an exchange, the federal government is required to do so.
Some Republicans have supported the concept, because it is market-based, and most states have moved ahead with plans to set up the exchanges, including states where Republicans are in control.
The exchanges, the White House said in its veto-threat message, "will allow Americans to compare prices and health insurance plans and decide which quality, affordable option is right for them." It cited Congressional Budget Office estimates that the Upton bill would deny the states $1.9 billion between 2012 and 2015 to establish exchanges and that some half a million people who would be covered under current law would go without health insurance if the bill passes.
The second bill, sponsored by Rep. Michael Burgess, R-Texas, would repeal mandatory funding for school-based health center construction. The budget office estimated that the bill would reduce direct federal spending by $100 million in the 2012-2016 period."
"I wish we didn't have to go at it $100 million at a time," Burgess said of his opposition to the health care law, "but if that's what we got to do, that's what we got to do."
The White House, while not threatening a veto, said the administration was open to working with Congress to improve the health care law but that the Burgess bill, "rather than making refinements to improve the law ... simply proposes to eliminate funding."
House Republicans, who made opposition to the health care law a central issue in their successful drive to capture control of the House in the November elections, moved to overturn the law in one of the first votes of this session. They also tried to eliminate money for implementing the law as part of legislation to keep the federal government running through the end of this budget year.
With those efforts making no headway in the Senate, GOP leaders vowed to also pursue a piecemeal approach. Last month the House voted to eliminate a section in the law that funds preventive health programs for such things as fighting obesity and reducing smoking.
The CBO estimated that the government would save $16 billion over the next decade by shutting down the program. Supporters said preventive care programs could save the government billions in health care costs.