The amount of time you have to re-efile a rejected return is specific to the state you live in.  Here is an awesome website you can go to see what your specific state rules are  https://cs.thomsonreuters.com/ua/ut/e-file-guide/us-map.htm 

Penalties only accrue if you don't pay your tax due before the 15th, it is not connected to your e-file being accepted or rejected.  So if you don't owe taxes you definitely won't get a penalty.  If you do owe taxes ensure to make a payment or set up a payment plan with the state taxing authority before today to ensure you don't accrue any penalties.