what are the days to refile and/or mail after rejects?

[JenMO]

Is there extra time to mail a return if it the efile rejects and there is no way of fixing?

[David1980]

Answer for the states will probably be all over the place. Answer for fed from Pub 4164:

1.4.2 Perfection Periods for Rejected Submissions
When a transmitted electronic business return (except excise returns 2290, 720, and 8849) is
rejected for Processing Year 2010 and subsequent Processing Years, there is a ten day
Transmission Perfection Period (look back period) to perfect that return for electronic retransmission.
When a previously rejected electronic return is “Accepted” by the IRS within the
ten day Transmission Perfection Period, it will be deemed to have been received on the date of
the first reject that occurred within that ten day period. Publication 4163 has detailed perfection
period information for MeF business returns.
The transmission perfection period for an extension to file, Form 4868, 7004 or 8868, is five
days.
The following transmission dates pertain to individual returns:
• April 20, 2014 – Last day for retransmitting rejected timely filed Form 1040 family
returns.
• June 20, 2014 – Last day for retransmitting rejected timely filed Form 1040 family
returns and/or Form 4868 extensions to meet overseas exception and Form 2350.
• October 20, 2014 – Last day for retransmitting rejected timely filed Form 1040 family
returns on extension from Form 4868.
See Publication 1345 for additional information on transmission timeframes for individual
returns/extensions.

And from Pub 1345:

Resubmission of Rejected Tax Returns
If the IRS rejects the electronic portion of a taxpayer’s individual income tax return for processing, and the ERO cannot rectify the reason for the rejection, the ERO must take reasonable steps to inform the taxpayer of the rejection within 24 hours. When the ERO advises the taxpayer that it has not filed the return, the ERO must provide the taxpayer with the business rule(s) accompanied by an explanation. If the taxpayer chooses not to have the electronic portion of the return corrected and transmitted to the IRS, or if the IRS cannot accept the return for processing, the taxpayer must file a paper return. In order to timely file the return, the taxpayer must file the paper return by the later of the due date of the return or ten calendar days after the date the IRS gives notification that it rejected the electronic portion of the return or that the return cannot be accepted for processing. Taxpayers should include an explanation in the paper return as to why they are filing the return after the due date.