The Health Exchange Security and Transparency Act was approved by a vote of 291-122, with 67 Democrats voting for the bill, The Hill reported.
The one-sentence bill would require the administration to notify users of healthcare exchanges within two days of a breach that their information may have been compromised.
Republicans said there is no such requirement under current law.
Rep. Darrell Issa, R-Calif., chairman of the House Oversight & Government Reform Committee, said a senior official with the Centers for Medicare and Medicaid Service warned in September against launching the site because of security concerns.
Democrats said the statement, made in a memo by Teresa Fryer, the chief information office for CMS, had been taken out of context and was an attempt to create fear about the website.
Rep. Elijah Cummings, D-Md., the top Democrat on Issa's committee, said Fryer's memo was a draft that had not been sent to anyone, including her supervisor.
The White House said it opposed the bill because it would create "unrealistic and costly paperwork requirements." The administration said it already had plans to tell people whose information was on the site if their information was breached.
Senate Democrats are unlikely to consider the bill.