CEO: "We've kicked the tires on this system"

Open enrollment for Obamacare begins today 03:07

Obamacare enrollment will be open for the next three months, giving Americans a second chance to register for federal health insurance.

One of the biggest issues with the roll-out the first time around was the website, which crashed almost immediately after launch and continued having problems after that.

But the site has since had an overhaul and CEO Kevin Counihan says this time, things should be much smoother.

"We've had multiple ways in which we've kicked the tires on this system, both internally and externally, to see that it works and that it's stable," he told CBS News.

Obamacare has 7 million customers, reducing the number of people without health coverage.

Wall Street Journal reporter Louise Radnofsky says that number's about to increase, as are prices.

"There are more plans in more markets this year, but that's affecting prices that people might see," she said. "Big plans that snapped up a lot of consumers last year are raising prices. At the same time, some of the new market entrants are making aggressively low bids to try to undercut them, which in turn affects the value of people's tax credits. They're actually going down in many states."

Radnofsky says consumers should go directly to

"They have to go back to the website to shop," she said. "It's very important they do it not just to get a better option but to avoid getting a worse one."

According to Radnofsky, people have until December 15 to make changes to their coverage that could take effect January 1, 2015.

"That's a real key deadline for people who bought last year around," she said.

For people who don't have coverage currently, they have until February 15 to register.

Radnofsky stresses that there are still 30 million Americans who are not insured.

"Some of them are not eligible to use the website at all to shop because they're not in the country legally," she said. "Some people have to have incomes that are too low to quality for tax credits towards the cost of coverage, because they live in states that aren't expanding their Medicaid programs. And some people have money, would qualify for tax credits or even wouldn't, but don't feel like the insurance options available to them represent a good deal. They may be opting to pay the penalty this year."

The law is headed to the Supreme Court for the third time around, which Radnofsky says is over "the tax credits that the law provides in exchanges."

She added, "There's a debate over whether people who live in states that did not run their own exchange that turned over some or all of that tax to the federal government can get those credits. And that's more than 30 states potentially affected."