The next deadline is March 31, which is when ACA open enrollment ends. Applications submitted between March 16 and March 31 will have an effective date of May 1.
If you do not meet the March 31 deadline, you may not be able to buy private health insurance until the next open enrollment period starts. The next open enrollment period will be November 15, 2014 to February 15, 2015.
The only way you can buy a health plan outside open enrollment is if you qualify for a special enrollment period.
The federal government requires all individuals and families to have health insurance, either through the federal marketplace or through an employer.