Obama has faced a tsunami of criticism over this month's sputtering debut of healthcare.gov, through which millions of Americans are expected to buy insurance.
Customers have had trouble signing on, getting accurate cost estimates, and completing enrollment.
"As you may have heard, the site isn't working the way it's supposed to yet," Obama said in his weekly broadcast address.
"That's frustrating for all of us who have worked so hard to make sure everyone who needs it gets health care."
Obama said the site had been visited more than 20 million times, and nearly 700,000 people have applied for coverage -- proof, he said, of the high demand for "quality, affordable health care choices."
"And that's why, in the coming weeks, we are going to get it working as smoothly as it's supposed to. We've got people working overtime, 24/7, to boost capacity and address these problems, every single day."
Obama's Republican opponents, who have long opposed his health insurance reform, seized on the website's failed launch as a chance to slam the administration.
At a House hearing Thursday, Republicans took turns bashing the administration and demanding accountability for the flawed website debut.
It was "interesting to see Republicans in Congress expressing so much concern that people are having trouble buying health insurance through the new website," said Obama Saturday.
"Especially considering they've spent the last few years so obsessed with denying those same people access to health insurance that they just shut down the government and threatened default over it."
Obama said he would work with opponents to improve the law -- formally known as the Affordable Care Act -- but that "it's well past the time for folks to stop rooting for its failure."
Some people "have poked fun at me this week for sounding like an insurance salesman," Obama said. "And that's okay. I'd still be out there championing this law even if the website were perfect."
On Friday, Jeffrey Zients, Obama's point man in the project, told reporters in a conference call that the administration had hired a general contractor to fix the website, and that the site should be running smoothly by late November.
"It will take a lot of work, and there are a lot of problems that need to be addressed," Zients said, according to participants in the call. "But let me be clear: healthcare.gov is fixable."
Obamacare requires most Americans to have health insurance from 2014 or face a fine, but the White House said it will give an extra six weeks, until March 31, to obtain insurance before facing the penalty.
Contractors argued the site's complexity -- it links millions of customers to federal and private databases like those of the Social Security Administration and 170 insurance firms -- was a key factor in its poor start.