WASHINGTON (CNN) -- After President Barack Obama's mea culpa over the disastrous Obamacare rollout, the fallout is still reverberating within his administration, on Capitol Hill, in insurance company boardrooms and in living rooms across America.
After the President's news conference on Thursday during which he said he "fumbled" the Affordable Care Act's launch, he immediately resumed his public relations tour touting the measure -- his signature domestic policy achievement.
"We're not going to gut the law. We're going to fix what needs to be fixed," Obama said in Cleveland.
Friday, he was back at the White House working to keep his promise to address its shortcomings.
He was scheduled to meet with insurance executives whose help he needs to carry out freshly announced rules that would allow those receiving health policy cancellations due to Obamacare to keep their plans for another year.
Despite Obama's apology and efforts to make amends for saying previously that Americans wouldn't lose coverage under the law he championed, a couple of moderate Democrats in the Senate said they would still push for a legislative fix that goes a little further than the administrative steps outlined by the President on Thursday.
"I feel deeply responsible for making it harder for them," Obama said on Thursday about Democrats who supported his bill and now face tougher reelection bids because of the law's difficult beginning.
Vice President Joe Biden planned to join one of those Senators, Kay Hagan of North Carolina, at a campaign event on Friday.
But Democrats who lead the Senate have indicated, however, that they will not bring up new Obamacare legislation for a vote for the moment, wanting to first see how the President's approach works.
In the House, the story is different.
The Republican-led chamber is set to vote Friday on a plan offered by Republican Rep. Fred Upton of Michigan that would address the policy cancellations.
Upton's bill, however, goes much further.
Instead of offering a year extension only for consumers who buy insurance on private, individual markets -- those mainly experiencing cancellations now due to the new law -- Upton's proposal would allow anyone to purchase those plans that are likely cheaper but don't meet coverage demands spelled out under the Affordable Care Act.
Upton's bill matters because Democrats, who also backed Obamacare when it was passed in 2010, are feeling the political heat a year ahead of midterm elections. They could take the opportunity to back the Upton bill for political cover.
Despite the administration's insistence that the House GOP plan would undermine Obamacare, the thinking goes that a "yes" vote would allow vulnerable Democrats to look as if they are taking action and not relying on the word or actions of a President whose credibility on the issue has taken a big hit and whose standing with the public overall has also suffered.
All this as the Upton bill itself has little, if any chance, of becoming law with the Senate taking a wait-and-see approach to begin with and not likely to take it up even if it decides at some point to pursue legislation.
Still, if a sizable number of Democrats back the Republican bill, it indicates they are becoming more uneasy with the health care law and Obama as presidency with three full years remaining in his second term.
Republicans: We told you so
Republicans have spent much of the past three years attempting to defund and dismantle Obamacare as unworkable and an illegitimate law since it was rammed through by a Democratic Congress without their backing and then signed by a Democratic president.
They have held hearings and investigations and the House has had dozens of votes to weaken or repeal it. Now, GOP lawmakers are seizing the moment with the law under fire to effectively say "we told you so."
House Speaker John Boehner recently called Obamacare "a failure" and Democrats risk supporting it further at their political peril.
The White House did not mandate the changes on policy cancellations but asked insurance companies to take the lead and offer extensions.
Health insurers, as represented by the America's Health Insurance Plans trade group, warned that last-minute changes in the law could "destabilize the market and result in higher premiums."
The individual policy contracts that are most affected comprise about 5% of the overall insurance market.
At least one major insurer, Aetna, said it would allow for extensions, but put the burden on state insurance commissioners to approve the changes.
These entities regulate industry and usually look out for consumer interests. They determine coverage standards and benefits.
State insurance commissions
The reason for many cancellations was that affected plans didn't meet new federal standards for minimum coverage requirements under Obamacare. This includes preventative care, maternity care and mental health care.
Washington State indicated that it would not allow for a year extension, saying that it is too complicated and disruptive at this late date.
More than canceled insurance plans
Canceled policies is not the only headache for Obama.
The federally run website where consumers can purchase insurance, HealthCare.gov., barely functioned on its launch October 1.
While improvements have been made, problems continue, making it difficult for people to enroll and browse plans offered by private companies.
Including similar online exchanges offered through 36 states, overall Obamacare enrollment numbers for the first month underperformed with only 106,000 signing up for coverage.
That's far from the seven million over time that experts anticipate will be needed to ensure that Obamacare works economically. It relies heavily on younger, healthier participants to help cover the cost of insuring older people who need more health care services.
A bright spot, however, is the enrollment of Medicaid, which has been expanded in 25 states under the new law. Nearly half a million people have signed up for benefits under the federal health insurance program for the poor.
-- CNN's Deirdre Walsh, Dana Bash, Ted Barrett and Kevin Liptak contributed to this story
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