The IRS says refunds are not being delayed. "More than 9 of 10 refunds are issued in less than 21 days," the agency said in a statement to CNNMoney. "Refunds are going out under our normal processes, and there are no systemic delays specifically related to [Affordable Care Act] issues."

The best way for filers to check their status of their check is to use the Where's My Refund? site, according to the IRS. Representatives can only do further research if it's been more than 21 days.

Though 21 days have yet to pass since the start of the tax filing season, some early filers are getting antsy because they usually receive their refunds more promptly. They are getting their transcripts through, which shows them codes associated with the processing of their return. Many are seeing TC 570, which indicates the refund is frozen while the return is being examined.

Up to 6 million Americans could be subject to the Obamacare penalty, according to Treasury Department estimates. But not every filer who has already paid the penalty is seeing their refund held up.