Open enrollment for Obamacare, or the Affordable Care Act, begins today. Problems with the law mean consumers could face significant rate hikes in some parts of the country. There will also be fewer health plans to choose from.

Starting today, the administration will make a major enrollment push -- but that may be a tough sell in states like Tennessee, which has seen premiums spike more than 50 percent, reports CBS News correspondent Margaret Brennan.

Insurance broker Eric Jans CBS News

For songwriter Wendy Jans and her husband, Eric, life was sailing along until health insurer Blue Cross Blue Shield pulled out of the Obamacare market in Nashville.

Eric, an insurance broker, said he panicked “a little bit.” Most of his 300 clients were covered by Blue Cross.

“Your clients, can they still afford health care?” Brennan asked.

“A lot of them are really nervous right now. Really nervous,” Eric said.

Eric was also paid by Blue Cross, income he has now lost along with his own family’s insurance.

“As of January 1, unless we jump on to something else. ... and we’re looking at $750 a month this year to $1,100 next year,” Eric said.

That’s $1,100 for a family of four.

Blue Cross Blue Shield left the Obamacare exchange in three major Tennessee markets citing a loss of $500 million over three years. That leaves 73 of the state’s 95 counties with only one insurer -- and average premiums up more than 50 percent. Other major insurers including Aetna, UnitedHealth and Humana have also exited markets in other states.

One key reason: not enough young, healthy people signed up to offset the sicker population, leading to losses for insurers.

Health and Human Services Secretary Sylvia Burwell argues that the problems are fixable.

She points to Obamacare’s successes: 20 million people have health insurance today who didn’t before the law was passed. The uninsured rate is now the lowest ever.

Health and Human Services Secretary Sylvia Burwell CBS News

To improve the market -- and lure back insurers -- the administration hopes to enroll nearly 14 million more people. They’re aggressively targeting millennials.

“But do you expect those insurance providers that have pulled out to come back?” Brennan asked.

“You know, I think a number of them will. I think a number of them will over time as they look and see what happens in the marketplace,” Burwell said.

“Any promises in the new year that any of them will rejoin the market?” Brennan asked.

“You know, at this point, I don’t think any of them have made those kinds of decisions,” Burwell responded.

Burwell said most Americans can get a plan for $75 or less a month, especially if they’re low income. They’ve launched a social media campaign to target community college students, recent immigrants and freelancers.