Citing administration officials it did not name, NBC said it was not immediately known whether delaying the individual mandate would require congressional approval or could be done administratively by the Department of Health and Human Services.
Currently, the law requires individuals without health insurance to begin the process of applying for insurance by Feb. 15 through the HealthCare.gov website, NBC said.
The report came as a spokesman for U.S. Sen. Joe Manchin, D-W.Va., said Manchin was drafting legislation to delay the mandate for one year, and Sen. Jeanne Shaheen, D-N.H., called for extending the open enrollment period.
HHS Secretary Kathleen Sebelius, Centers for Medicare & Medicaid Services Director Marilyn Tavenner, along with White House Chief of Staff Denis McDonough and senior adviser Valerie Jarrett, met Wednesday at the White House with health insurance chief executive officers and lobbyist Karen Ignagni, president of the America's Health Insurance Plans trade association.
The White House said in a news release the administration officials were "collaborating closely with the insurers to address problems" with ACA enrollment.
The statement said the meeting with chief executive officers of companies including Aetna, Humana, CareFirst, Health Net Inc., WellPoint and Kaiser Permanente "is another way we are ensuring that we are doing everything possible to address the technical issues to ensure that all the American people who need it can purchase the affordable health care coverage made available as a result of the Affordable Care Act."
Sebelius told CNN Tuesday President Obama did not know HealthCare.gov faced technical problems before it went live Oct. 1.
"I think it became clear" to Obama in "the first couple of days," she said.
"I think that we talked about having testing going forward," she said of White House and HHS discussions before the site went public.
"If we had an ideal situation and could have built a product in a five-year period of time, we probably would have taken five years," she said. "But we didn't have five years, and certainly Americans who rely on health coverage didn't have five years for us to wait. We wanted to make sure we made good on this final implementation of the law."
The federal website -- for residents of the 36 states that chose not to create their own state healthcare exchanges, where individuals and small business can buy private insurance plans -- has been marred by serious technological problems from its debut, making it difficult to sign up for health insurance.
Some insurance companies are reported to have expressed concerns the site wouldn't be ready to go live, and The Washington Post said the site failed to accommodate even a few hundred users in a test run just days before the rollout.
House Democrats are separately to meet with HHS Office of Health Reform Director Michael Hash about the technical problems.
Several Republicans, including House Budget Committee Chairman Paul Ryan of Wisconsin and Sen. Ted Cruz of Texas, have called on Sebelius to resign over the problems.
"I think this rollout has been a fiasco, not just because they have bad tech but because the law itself is so fundamentally flawed," Ryan said in a conference call Tuesday in support of the gubernatorial campaign of Virginia Attorney General Ken Cuccinelli.
"We gave the administration every chance to delay the law and delay the mandate," Ryan said.
But Sebelius told CNN she hadn't talked with Obama about resigning.
"What I talked about is doing the job that I came here to do," the former Kansas governor said. "This is the most important work I've ever done in my life, delivering on an historic act, making sure that we have health security for the millions of Americans."
As part of that, Sebelius announced Tuesday she hired incoming National Economic Council chief Jeffrey Zients to lead the so-called tech surge to fix the troubled website.
Sebelius also said her department recruited other "experts and specialists drawn from within government, our contractors and industry, including veterans of top Silicon Valley companies" and Presidential Innovation Fellows, to fix HealthCare.gov.
She did not name or enumerate the others, nor did White House spokesman Jay Carney when asked by reporters.
Presidential Innovation Fellows, established in August 2012, brings "top innovators from outside government for focused 'tours of duty' with our best federal innovators on game-changing projects," the White House says on the program's website.
The program's projects seek "to deliver significant results within six months," the site says.
Zients, the U.S. chief performance officer and a former acting director at the Office of Management and Budget who once worked for Mitt Romney's Bain & Co. investment firm, is scheduled to join the White House Jan. 1 as National Economic Council director, replacing Gene Sperling.