"The American people are tired of all the broken promises from the Obama administration—from the millions who've had their insurance dropped, to the increase in the cost of their health plans and that many won't be able to keep the doctors they've come to trust," Sen. Orrin Hatch of Utah, top Republican on the Finance panel, said Tuesday.
Sebelius testified a week ago to the Republican-run House Energy and Commerce Committee.
At that confrontational session, she apologized for the troubles dogging the website where uninsured Americans and those buying coverage privately are supposed to be able to purchase health insurance. The secretary, who numerous Republicans have said should resign, has promised the site would be fixed by the end of this month and says it is secure.
Insurers are sending cancellation notices to customers whose current policies lack enough coverage to meet the law's more demanding standards - at least 3.5 million Americans, according to an Associated Press survey of states.
(Read more: POLL: Should Sebelius go over Obamacare glitches?)
The Obama administration has said people facing cancellations will be able to find better coverage from their current insurance company or on state or federal exchanges where competing policies are being offered.
Lawmakers of both parties have introduced rival bills that would let people retain their existing health insurance policies. But administration officials refused to state their views Tuesday on those proposals.
White House spokesman Jay Carney suggested the White House would resist letting insurance companies continue offering substandard plans, saying that would undermine the law's fundamental promise of better health care.
"We're focused on implementing the Affordable Care Act," Carney said, using the law's formal name.
Senate Majority Leader Harry Reid, D-Nev., kept his distance from a measure by Sen. Mary Landrieu, D-La., who faces re-election next year, which would force insurers to reinstate canceled policies.
"There are hundreds of bills introduced every week, and we have to sort through those that have opportunity to be voted on," Reid said.
On the defensive about the law, Democrats have started trying to refocus Americans on its benefits.
The law requires most Americans to have health coverage by the start of 2015 or face fines. Middle-class people who don't get health insurance at work will qualify for federal subsidies for the private coverage they buy. More lower-income people will qualify for Medicaid in states that have agreed to expand that federal-state health care program for the poor.
"The real train wreck is what people are experiencing every day because they can't afford care," Sen. Tom Harkin, D-Iowa, said Tuesday at a hearing of the Senate Committee on Health, Education, Labor and Pensions, which he chairs.
At that hearing, Marilyn Tavenner, who runs the agency most directly involved in implementing the health care law, said that nearly 700,000 applications have been submitted at federal and state marketplaces in the law's first month of operation. She said technicians are making improvements that have already made the website faster.
"We obviously underestimated demand," said Tavenner, who heads the Centers for Medicare and Medicaid Services. She added, "We obviously had more bugs than we realized."
—By The Associated Press