President Barack Obama's healthcare law may have had a shaky rollout and was never short of opposition and criticisms, but as of Monday, the last day of the first annual sign-up period to avail of health insurance under the Affordable Care Act, the healthcare law will likely reach a milestone as it could hit the goal of signing up 7 million Americans in private health insurance.

Last week, the Obama administration said that as of March 27, six million people have already signed up for the Affordable Care Act and that the healthcare.gov site, the federal government's official enrollment site, has been receiving one million visits per day.

The Centers for Medicare & Medicaid Services, the federal agency in charge of the Affordable Care Act's rollout, said that millions of people have been visiting healthcare.gov and calling the Health Insurance Marketplace call center days before the March 31 deadline.

"Over the past week the site has handled record consumer demand well - supporting more than 8.7m visits since last Sunday, with 2 million alone this weekend," the federal agency said in a statement. "The 24/7 call center that supports the Health Insurance Marketplace has taken a record number of calls from consumers - in the last week alone the call center took more than 2.5 million calls, compared to 2.4 million for the entire month of February."

If the number of calls and website visits are successfully converted into people actually signing up and availing of health insurance, the healthcare law's goal of seven million sign-ups may be within reach.

"The traffic and energy and interest this weekend shows many more are interested in the coverage," said White House spokeswoman Tara McGuinness.

Senator John Barrasso, a Wyoming Republican, is nonetheless skeptical.

"I think they're cooking the books on this," he said. "What kind of insurance will those people actually have? Will they be able to keep the doctor that they want? How much more is it going to cost them?"

Although the open enrolment ends before midnight today, the administration said last week that it will continue to accommodate those who have started their enrolment process before the deadline which means that it may take weeks before the final number of Americans who have signed up for Obamacare will be confirmed.