The administration has said that you can avoid the penalty if you sign up by April 15th and affirm that you couldn't use the website before March 31st.
There is no legal basis for that waiver. The administration has violated its own hard-won law in all kinds of ways trying to compensate for its failure to effectively implement it.
The Administration actually does have legal authority to execute various parts of the law as they see fit. It does undermine credibility and set a bad future precedent, however.