A number of states that operate health-insurance exchanges could allow consumers to buy coverage for 2014 after next Monday's deadline.
Part of the reason is that some states are sill suffering technical problems, including Nevada and Oregon.
The new extensions would follow the massive delays and technical problems that hit the launch of Obamacare late last year.
The federal government hasn't yet said whether those purchasing plans on its Web site will receive more time.
Consumers who don't buy coverage for next year face fines of $95 or 1% of their incomes.
Meanwhile, insurers around the country are on a drive to sign people up.