Monday, Dec. 23, is the deadline to sign up for insurance plans through the new federal healthcare exchanges that take effect on New Year's Day.
The Affordable Care Act, commonly known as Obamacare, was intended to make healthcare more accessible but has struggled to be implemented because of continuing glitches.
"It has been very frustrating for many Alaskans and frustrating for us," said Tyann Boling, Enroll Alaska's chief operating officer.
She said glitches in the website meant Alaskans had a small window to sign up for coverage.
"Essentially it did not work for two months," Boling said. "I'm going to be pushing really hard, writing letters and doing everything I can, to get a law for some sort of extension because we need more time."
The deadline has already been pushed back.
Nationally there are concerns that a rush of last minute sign-ups could cause problems for the website again.
Obamacare has long been the center of a partisan battle.
Many Republicans believe the program is a failure. Sen. Tom Coburn, R-Oklahoma , said the problems are so severe they cannot be fixed without a new law.
"What I would say is we need to change healthcare," Coburn said. "But what they've done, you can't fix this mess."
Democrats believe that the program is still worthwhile even with the missteps.
"The bottom line is there are a lot of good things in Obamacare that people like, and the more people see that, the more positive it's going to be," said Sen. Charles Schumer, D-New York.
About 600 Alaskans have signed up for plans via the insurance marketplace.
Enroll Alaska said they want to see more people sign up for coverage for the first time or to find a cheaper plan
"We're definitely there to help people and we get them enrolled, but it's definitely not a simple process,"