WASHINGTON — President Barack Obama’s handling of his signature health-care law is triggering a rebellion by some House Democrats who could back a Republican measure to allow Americans to keep their insurance plans through next year.

House Democrats confronted David Simas, the deputy senior adviser to the president, and Mike Hash, the director of the Office of Health Reform at the Department of Health and Human Services, during a closed-door meeting Wednesday, lawmakers said.

With thousands of individuals receiving notices that their current insurance policies would be canceled as noncompliant with the Affordable Care Act, some Democrats are pushing the administration to come up with remedies before Nov. 15. That is when the House is scheduled to vote on the Republican bill.

“A lot of Democrats are very upset that this happened, number one, and urging for there to be an immediate fix for it,” Rep. Patrick Murphy, D-Fla., told reporters after the meeting. The Obama aides said the administration is working “24/7” on a solution, Murphy said.

Obama’s health-care rollout has been beset with malfunctions impeding consumers’ ability to sign up on websites, questions about the security of private information, and complaints by individuals who are losing their insurance plans and face premium increases for new policies.

BOEHNER SEES ‘SYMBOL OF FAILURE’

The Obama administration indicated it was willing to consider amending the health-care law to halt some of the hundreds of thousands of insurance policy cancellations that have raised alarms among voters and lawmakers.

About 106,000 people in the United States signed up for private health insurance through Obamacare last month, and 396,261 for Medicaid plans, according to data released Wednesday. The government had an early target of about 800,000 sign-ups in private plans for the first two months.

House Speaker John Boehner, an Ohio Republican, said the numbers were a “symbol of failure” for the law.

“These numbers underscore the urgent need for President Obama to allow people to keep the plans they have and like,” Boehner said in a statement.

Senate Democrats will meet Thursday with White House officials, including Denis McDonough, Obama’s chief of staff, according to a Senate Democratic aide who requested anonymity because details haven’t been announced.

“I’ve been frustrated from the beginning, from issues with the website to misunderstanding how to move this issue forward,” said Sen. Mark Begich, an Alaska Democrat seeking re-election next year.

Senate Minority Leader Mitch McConnell, R-Ky., said he sees a “stampede” of Democrats moving away from Obamacare.

Majority Leader Harry Reid, D-Nev., told reporters he had a “long conversation” with Obama Tuesday and was “very comfortable” that the website troubles “will be fixed.”

Sen. Joe Manchin, D-W.Va., said changes he and fellow Democrats were suggesting were to fix the law, not repeal it.

“I don’t think you want to go back to where people are one illness away from being bankrupt,” Manchin told reporters today. “But on the other hand, I don’t think anyone expected someone to take their insurance away from them.”

Rep. John Yarmuth, D-Ky., said the White House is expected to propose fixes to party leaders by tomorrow, the day before a planned vote on a measure written by Fred Upton, a Michigan Republican. Absent any fixes, Yarmuth said he would vote for Upton’s measure.

OPTIONS UNDER SCRUTINY

“I agree with those who stood up and said that it’s going to be difficult for a lot of Democrats to vote against it unless there is a viable option from the administration,” Yarmuth said in an interview.

The Obama administration opposes Upton’s measure because it would let insurers “sell new policies that were substandard” and undermine the Patient Protection and Affordable Care Act, White House press secretary Jay Carney told reporters Wednesday. Obama is discussing with lawmakers ways to improve the measure and will have an announcement “sooner rather than later,” Carney said.

A more limited proposal, from Louisiana Democratic Sen. Mary Landrieu, “shares a similar goal with what the president is exploring,” and the administration isn’t ruling out a legislative remedy, Carney said.

Landrieu, who is seeking a fourth term in 2014 in a state Obama lost last year by 17 percentage points, introduced a measure requiring that individuals be allowed to keep their health plans as long as they stay up-to-date on payments.

Five Democratic senators are co-sponsoring the measure.