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Mr. Obamais facing political heat because he repeatedly promised that people who liked their health plans could keep them, a claim that is proving untrue for millions of Americans. Some of these enrollees say they are facing higher premiums on the exchanges.

Sen. Lamar Alexander of Tennessee, the committee’s ranking Republican, said there should be broad support for legislation that would let people keep their insurance plans, even if the coverage doesn’t meet Obamacare’s standards.

Ms. Tavenner told Congress on Tuesday that yearly “churn” in the individual insurance market is common and that the law offers consumers more protections and subsidies to help them afford coverage.

A pro-Obamacare group, Get Covered America, highlighted a married pair of full-time artists in New Mexico who received a cancellation notice for their $250-a-month catastrophic plan, but found a better bronze-level plan on the exchanges that will cost them nothing — because of Obamacare’s subsidies.

Supporters and critics of the law are making their cases through cherry-picked anecdotes, but GOP lawmakers say the number of Americans dropped from their plans cannot be ignored.

“It’s not what the president promised, and it’s not the kind of health reform Americans asked for,” Senate Minority Leader Mitch McConnell, Kentucky Republican, said Tuesday on the Senate floor. “So we should keep our focus where it belongs — on the real people getting hurt by this law.”

House Republicans are raising questions about the security of the overall program, highlighting “War Room” notes requested by Oversight Government Reform that refer, briefly and cryptically, to possible cases of navigator fraud in Kansas and Ohio.

Ms. Bataille, of CMS has dismissed the documents as “meeting notes” and not official records.

“I am not aware of any instances of suspected fraud that have been reported,” she told reporters.

Other complaints were state-specific. Sen. Lisa Murkowski, Alaska Republican, said nightly maintenance on from 1 a.m. to 5 a.m., EST, doesn’t jibe with her constituents’ needs. In their time zone, the daily shut-down occurs right after parents put their kids to bed and have the time to review their insurance options.

Democratic Sen. Barbara A. Mikulski, Maryland Democrat, said she wants the law to work, but needs to see more clarity and outreach from the Obama administration.

“What I worry about is that there’s such a crisis of confidence, people won’t enroll and the very people we need to enroll — particularly our young people — to make this whole system work won’t happen,” she said.