But not all states or insurers have taken up that option, or maintained it for their customers.
Although Karlson's non-compliant plan was allowed to continue in Obamacare's first year, Aetna pulled the plug for 2015.
"As noted in the letter to our customer, we discontinued this plan, as we have others," said Aetna spokeswoman Susan Millerick. "Our intent is to offer individuals a selection of ACA-compliant plans. We believe the marketplaces now offer a stable experience that offers consumers the opportunity to shop, compare and buy plans and we also have been working with customers to find a new Aetna plan if they choose."
"We began this process in 2013 and have been updating our portfolio over time, so we have not been releasing specific information about the number of plans that have been discontinued, but I can tell you that this is a small subset of our individual customer base, which is a small portion of Aetna's overall membership," Millerick said.
Despite the big increase in price, Karlson was ready to stay with an Aetna plan.
That changed when he called a rep for Aetna "to check on something. That was when the person I spoke to said, 'Oh, just so you know, there's no out-of-network coverage,' " Karlson recalled.
In other words, he'd have to pay out of pocket for any doctors who weren't in Aetna's network of providers.
That was a problem for him because "a good deal of our doctors are out of network" and their services had been covered by the old plan, Karlson said. By this time, it was Dec. 12, three days away from what he believed to be the sign-up deadline.
He reached out to someone he knew who had dealt with insurance before, who referred him to an investment adviser name Brett Sigler, of Client Focused Advisors in New York. Sigler and his colleagues last year got certified as brokers for the New York State of Health.
Sigler told CNBC that while "we saw there was an opportunity where a lot of people were going to need help," other than putting out the word in a networking group he was associated with, he didn't really solicit business actively.
Despite that, Sigler's gotten Obamacare business this year from Karlson and about 100 other people, essentially from word of mouth.
"It's been way more than I anticipated," Sigler said. "I'll get calls from people that I've never met before."
Read MoreHealthCare.gov enrollment hits nearly 2.5M
"I've seen a lot of frustration with just how complicated the whole process is. Their plans were just uprooted, and they get looking into figuring out what they should be doing," Sigler said. "The website can be intimidating for people to figure out."
"My last two weeks have been insane," he said, referring to the number of health insurance sign-ups he has handled. He noted that about 15 people contacted him past the original Dec. 15 New York deadline for coverage as of Jan. 1, with some unaware when the deadline was, extended or otherwise. The final open-enrollment deadline for any 2015 coverage is Feb. 15.
Sigler worked with Karlson and got him a new family plan that costs $1,221.60 per month from Health Republic Insurance, a co-op, or consumer-operated and -oriented insurer that was started to serve the new Obamacare market.
On Monday, after having enrolled in the new coverage, Karlson said he felt somewhat ambivalent about the experience of having had to purchase an Obamacare plan.
"It's like, I'm happy that I have insurance, but I wish I could have the insurance that I want," he said. "I feel I can adapt to whatever I have, and we are, but, I guess it's like I didn't realize I had a good thing."
Karlson said he and his wife were talking about getting appointments for some of their existing doctors before the New Year, in the event they never are able to go to them again with coverage under the new plan. "I'm just kind of annoyed that it's not as simple as it once was," he said.
—By CNBC's Dan Mangan.