I just started a new job and they will not let me enroll to the health insurance I will be getting until March 1st. Will I get penalized for not having 2 weeks of health insurance? Or do I need to buy health insurance for two weeks? Will companies cover me for only two weeks? My job won’t let me fill out the paperwork until March 1st.
You can go less than three full months without coverage. If you miss more time, but do get covered, only the first two months are exempt. In your case you will owe the fee for one month. However, you may be able to get around this by applying to the Marketplace. Exemptions can change each year, in the past there has been exemption for those who signed up for the Marketplace but had trouble enrolling, but as a general rule of thumb one must enroll during open enrollment (unless they have a life event that qualifies them for special enrollment).
Check with your employer about start dates. Typically there is a 90 day waiting period to enroll. If the start date of the coverage is any later you can consider getting a plan through HealthCare.Gov in the meantime. You can still get cost assistance up until the point that your employer coverage starts.
Learn more about coverage gap exemptions and other exemptions.
NOTE: To be clear, the coverage gap exemption is "less than three months" so one day short is fine, one day over and you owe the fee for the extra month. You are exempted from 2, and as long as you have coverage for 1 day in the third month you are safe (effectively then the exemption covers you for "less than three" but "almost three" months.