More than 6 million people have signed up for health insurance through the health law’s state and federal online marketplaces, or exchanges, since Oct. 1, the administration announced Thursday.

President Barack Obama, who is traveling in Europe, announced the number in a conference call with groups that are helping consumers sign up for coverage.

In a blog post, Centers for Medicare & Medicaid Administrator Marilyn Tavenner said  the health law’s web site, healthcare.gov, and 800 number, had near record traffic Wednesday, with 1.5 million visitors and more than 430,000 phone calls.

“With 4 days left for consumers to sign up for coverage, we are working hard to ensure that our systems can handle the unprecedented demand as people enroll before the March 31 deadline,” Tavenner wrote.

The Congressional Budget Office originally estimated that 7 million people would sign up for the exchanges by the end of the enrollment period. After computer problems botched the Oct. 1 rollout, the CBO revised that estimate down to 6 million. Federal officials have said they do not yet know how many people who have enrolled have paid their first month’s premium. Insurance industry officials have reported that about 70 to 80 percent of enrollees have paid.

Reaching 6 million has both practical and political significance. The more enrollees there are, the more likely the risk pool will be balanced between sick and healthy individuals. That calculus will be based on enrollments at the state and local levels where premiums are set, say experts. Republicans have expressed skepticism that the law would provide affordable coverage for millions of Americans and called for its repeal.