Some Democrats sought to substitute a plan of their own, which consisted largely of Obama's new policy, but it failed on a party-line vote.
Even so, the combination of the president's announcement and his party's alternative apparently siphoned off a large number of Democratic votes from the GOP measure.
In a veto threat Thursday night, the White House accused Republicans of seeking to "sabotage the health-care law," and said their measure would allow "insurers to continue to sell new plans that deploy practices such as not offering coverage for people with pre-existing conditions, charging women more than men, and continuing yearly caps on the amount of care that enrollees receive."
A veto would come into play only if both houses approve legislation and send it to the White House for the president's signature.
Political calculations were evident as Obamacare produced yet more controversy.
The political arms of both parties in both houses churned out attacks all week that underscored the importance of the issue in the 2014 elections. Additionally, Obama made an unusual attempt Thursday to shelter any Democrat who might have said when the bill was under consideration in 2010 -- as he did -- that anyone wanting to keep existing coverage would be permitted to.
"They were entirely sincere about it," he said of the lawmakers. "It's not on them, it's on us."
In the Senate, a handful of Democrats who face tough re-election races next year, led by Sen. Mary Landrieu of Louisiana, are supporting legislation to require insurance companies to renew policies canceled because of the law.
Under the law, plans are required to meet numerous conditions to qualify. Among them, they would have to accept all customers, regardless of pre-existing conditions, would be limited in additional premiums they could charge on the basis of age and could not cap lifetime benefits. They also would have to provide coverage in a wide range of areas -- doctor and hospital care for adults and children, laboratory services, preventive coverage and prescription drugs among them.
The cancellation issue is only part of the woes confronting the president and his allies as they struggle to sustain the health-care law.
Obama repeatedly has apologized for a dismal launch of www.healthcare.gov, which consumers in 36 states were supposed to use beginning on Oct. 1 to sign up for new coverage. The website is so riddled with problems that the administration disclosed earlier this week that fewer than 27,000 signups have been completed -- a number that Republicans noted is dwarfed by the flood of cancellations issued because of the law.
Compounding the administration's misery, the poor quality of the website has made it that much harder for consumers receiving cancellation notices to shop for alternative plans.
It is unclear what, if anything, the administration is prepared to do to alleviate the threat of a break in coverage for those consumers.