No. You should be able to file without the FED Tax ID number on the 1099-Misc for the MN Tax Rebate. Just be sure to label it as MN Tax Rebate in the interview section. You should, however, get a copy of the form for your tax records.
If that blocks the e-file/completion of your return here is a link to the MN Department of Revenue. Contact them and ask for the ID number and a copy of your 1099-Misc.
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