(CNN) - What a difference a day makes.
On Wednesday, House Democrats lit into White House officials who couldn't explain how President Barack Obama planned to make good on his failed promise that Americans could keep their health insurance under Obamacare if they preferred.
But by Thursday afternoon, rank-and-file members appeared to have cooled down after a closed-door session with White House Chief of Staff Denis McDonough.
He walked them through the administrative fix the President unveiled earlier in the day to help people whose individual health policies are being canceled primarily over tougher coverage requirements imposed by the Affordable Care Act.
"I can say almost unanimously that our members were very pleased with the President's statement today that he would do what he could do administratively on this," House Minority Leader Nancy Pelosi told reporters after the session.
She was referring to Obama's comments about his administration's temporary - for now - approach to remedy the problem by allowing people to hold onto their plans, if the insurance industry and the states go along.
House vote Friday
The Republican-led House, which sees the policy issue and the rocky rollout of the Obamacare website, HealthCare.gov., as proof the sweeping health care law as unworkable, will consider a bill on Friday to allow Americans to keep their plans. It also takes steps fiercely opposed by the Obama administration.
House Democratic leaders urged members to vote against the it. Although the GOP bill has some features similar to the proposal unveiled by the White House, Democratic leaders argued it was a step toward dismantling the health care law, Obama's signature domestic achievement.
Pelosi said Democrats plan to offer their own proposal on Friday, which will be "complimentary to what the President has done."
But that alternative does not have enough votes to pass.
Similar legislation has been proposed in the Senate, but the Democratic leadership is not eager to push ahead now that Obama has taken action and has signaled it is taking a wait and see approach.
A White House official said the one-year policy extension on cancellations is temporary that could go beyond next year, depending on how things play out.
The administration also said it is open to a potential legislative fix so long as any change would work and not undermine health care reform.
"We're not going to gut the law. We're going to fix what needs to be fixed," Obama said later on Thursday in Cleveland.
Meeting 'very impressive'
Maryland Democrat Elijah Cummings called the meeting with McDonough and his presentation "very impressive" and said he felt confident it would address concerns raised about people losing their coverage.
Another member said the mood at the meeting with McDonough was "vastly improved" from Wednesday's session with a senior Obamacare adviser, that they got answers to key questions this time.
At one point, members applauded McDonough's presentation. Questions focused on the proposed policy solution, with several pressing over how it would work in their states.
Cummings said he thought Obama's plan on cancellations was sufficient and that McDonough told them the White House had talked to the insurance industry and is not worried about companies being able to handle any changes.
McDonough's presentation also included two to three dozen specific improvements the administration had made to the website, which was designed to allow Americans to purchase insurance online. Three dozen states also have Obamacare purchase programs.
Virginia Democratic Rep Jim Moran told reporters instead of "rhetoric" at the meeting, Democrats were given "cold hard facts in terms of operational achievements."
Midterms a year out
The policy snafu and the problem-plagued website made House Democrats nervous that the health law approved with only Democratic votes in 2010 was becoming a big political liability with midterms a year out.
Heads "should have rolled" at the White House over the website debacle, said Rep. Nick Rahall, who also is skeptical of Obama's plan on remedying cancellations.
Rahall, who is regularly targeted by Republicans in his West Virginia swing district, told reporters on Thursday that the health care debacle is hurting him in his reelection bid.
He said outside groups are running ads against him on the President's previous pledge on keeping health plans.
"I'm going to have to respond," he said.
Rahall is reviewing the Republican legislative proposal. Asked if it helps him at home that Obama went out of his way to try to take the blame for the health law's shortcomings, Rahall said "not really."
Another Democrat facing a tough re-election race, Arizona Rep. Kyrsten Sinema, planned to vote for the GOP bill.
"I just support any reasonable solution that allows Americans to keep their health care plans if they like them," she said.
Obama acknowledged on Thursday that the Obamacare problems has put a burden on Democrats whether they are up for reelection or not.
Asked if the President's proposal gives Democrats in 2014 enough cover, McDonough told reporters, "This isn't about elections."
CNN's Lisa Desjardins, Dana Bash, Jim Acosta and Kevin Liptak contributed to this report.