Nov. 29, 2013 -- Despite facing a disastrous rollout of his health care plan, criticism over his policies and approval ratings that have plunged to an all-time low, President Obama said he remains confident that his signature health care law will be an important part of his legacy and things can only get better.

"I've gone up and down pretty much consistently throughout," Obama told ABC's Barbara Walters in an exclusive interview at the White House. "But the good thing about when you're down is that usually you got nowhere to go but up."

Obama's Affordable Care Act,, which was meant to be a centerpiece of his presidency, has been hit with enormous backlash since its website, Healthcare.gov, went live in October and has continued to suffer from technical glitches. The race is now on for the tech-surge team to produce a fully functional website.

"I continue to believe and [I'm] absolutely convinced that at the end of the day, people are going to look back at the work we've done to make sure that in this country, you don't go bankrupt when you get sick, that families have that security," the president said of his health care law. "That is going be a legacy I am extraordinarily proud of."

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But in the aftermath of the website's troubled rollout, reports surfaced that senior Obama administration officials expressed ongoing anxiety over the site not working properly months before it went live on Oct. 1, but seemed to have left the president in the dark about their concerns.

"Obviously my most recent concern has been that my website's not working ... and we're evaluating why it is exactly that I didn't know soon enough that [it] wasn't going to work the way it needed to," Obama said. "But my priority now has been to just make sure that it works."

Since the rollout, Obama has been front and center, apologizing for "fumbling the ball" and not executing the rollout better. But Republicans continue to pounce on what has now been called a "broken promise" to deliver affordable health care to the nation. According to a ABC News-Washington Post poll released last week, the president's job approval rating fell to 42 percent, down 13 percentage points this year and 6 points in the past month to match the lowest of his presidency. Obama is also at career lows for being a strong leader, understanding the problems of average Americans and being honest and trustworthy -- just 41 percent rate him as a good manager.

Even still, Obama brushed off the notion that the American people think he is untrustworthy.

"I got re-elected in part because people did think I was trustworthy and they knew I was working on their behalf," he said, noting that every president goes through rough patches. "Very rarely are the good things that happen get the same attention as the things that aren't working so well."

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President Obama's job approval rating roughly matches that of President George W. Bush at the same point in his second term, according to recent polling, but again, Obama pressed that he isn't finished yet.

"Every president in their second term is mindful that you've only got a limited amount of time, and you want to make sure you are squeezing every last ounce of energy that you have to try to deliver on the commitments you made to the American people," he said.

Even faced with a firestorm of criticism, and recent incidents of the president being booed or heckled during speeches, First Lady Michelle Obama joked that even though her approval ratings are higher than the president's, she too had been booed before and told Walters it is just "part of the job."

"It's a hard job," the first lady said. "I am fortunate to be living with a man who has a long view of this job, who understands that, in the case of health care, that this is all about the folks who don't have insurance, the folks he sees every single day."

The Obamas, who just celebrated their 20th anniversary together, also talked about the strength of their marriage, and that in good times and bad, they have each other's back. No matter what lies ahead, the president maintained that Michelle is "his rock" and helps keep him in check. The first lady said she wants young people to learn from their story.

"You're going to have people who don't like what you do, but you better have your own vision, and you better have your own will and your own passion and determination," Michelle Obama said. "Know that life requires work and sacrifice and sometimes it's painful, but there is a lot of joy and there is a lot of hope and possibility."

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Though the president didn't speculate on who should be next to fill the role of Commander in Chief, Obama acknowledged that this country's first female president might not be too far off on the horizon.

"We have some amazing female [public] servants all across the country and there is no doubt that sometime very soon, we're going to have a female president," he said. "I'm confident that she will do a great job."

When asked if he thought the first lady would make a better president than he would, Obama laughed and said, "that's an easy question, but she is smart enough to know that she might not want to go through the process."

Michelle Obama said she couldn't do the job better than her husband.

"He has a level of patience and focus and tenacity and calm that just doesn't come by anyone," she said. "I definitely don't [have that patience]."

As the country celebrated Thanksgiving this week, the president shared a message he had for those who are still struggling to find work and pay the bills.

"Every day I'm going be working as hard as I can on your behalf," Obama said. "For all the challenges and all the polarization of our politics and the frustrations of Washington, this remains and will remain the greatest country on Earth."

"Americans, I think deep down, care about each other and want to do the right thing," he continued. "And we're going make sure that we do everything we can to help folks, who are out there working hard, trying to make it."