President Barack Obama's Democratic allies have begun voicing frustration with widespread problems with aspects of his signature healthcare law.
House Democrats have complained that technical issues with the insurance enrolment websites had overshadowed the law's current and future benefits.
Some demanded Mr Obama find and sack those responsible for the glitches.
Mr Obama has said technical problems with the site are "unacceptable" and pledges they will soon be fixed.
He assured Americans on Monday that technical experts from both inside and outside the government were working around the clock to fix the website and its underpinnings.
The health law, known formally as the Patient Protection and Affordable Care Act and informally as Obamacare, was passed in 2010 and is Mr Obama's foremost domestic policy initiative.
Among its central provisions are an expansion of the Medicaid public health programme for poor people, a requirement that Americans who do not have insurance from their employers or the government buy it on their own - with subsidies to aid the purchase, and a rule allowing children to remain on their parents' insurance until age 26.
Mr Obama and the law's supporters say it will eventually reshape America's costly and inefficient healthcare system and provide insurance to most of the estimated 46 million Americans who lack it.
Plagued with problems
At issue currently are websites run by the federal government and some states that serve as online marketplaces where individuals can compare private insurance plans, learn about available public subsidies, and sign up for a plan.
The sites, known as exchanges, opened on 1 October. The White House aims to enrol as many as seven million people through the exchanges by the 31 March end of the enrolment period.
The central site run by the federal government, healthcare.gov, has been plagued with problems, notably extremely long wait times. Websites run by individual states have not performed as poorly.
The Republicans, who have opposed the law from the beginning and have sought to undermine it at every turn, are now calling for the rollout to be delayed and for deadlines for enrolment to be pushed back.
The Republicans have also loudly demanded an investigation into the exchanges' shortcomings.
"It is our job to hold them accountable, and when it comes to Obamacare clearly there is a lot to hold accountable," House of Representatives Speaker John Boehner said on Wednesday.
In light of the technical difficulties, some Democrats have also said Mr Obama should consider extending the enrolment period beyond 31 March.
But House Democratic Leader Nancy Pelosi advised against that.
"I think we should try to fix what we have, move forward with the deadline we have," she said. "What we want to do is fix it and go forward with it, not make policies that are predicated on its not working."
Complaints from Mr Obama's fellow Democrats are a relatively new part of the debate.
Democratic members of the House of Representatives left a briefing provided by the administration on Wednesday saying they had resolved not to let the problems with one part of the rollout overwhelm the law's benefits.
"The president needs to man up, find out who was responsible, and fire them," Minnesota Congressman Richard Nolan said. "You don't get many second chances to get a good first impression."
The White House has sought to reassure political allies and Americans at large that the government is working to resolve the issues.
The Obama administration has launched what senior officials called a "tech surge", with senior economic aide Jeffrey Zients tasked with analysing and repairing the problems.
On Wednesday, executives from top health insurance companies agreed to form technical teams to help the Obama administration fix the website and the systems underlying it.
"We are collaborating closely with the insurers to address problems we have witnessed," the White House said in a statement, after executives from 14 insurance companies met Health and Human Services Secretary Kathleen Sebelius and other senior administration officials.