No. The service is funded by fees and as such is not solely dependent on government funding for operation. USCIS will be open.
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No it will not, because USCIS is a self sustaining (fee based) agency.
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USCIS itself should not be affected but their processing might be affected to the extent they have to rely on other federal agencies for information/ processing/ background checks/ etc and to the extent those federal agencies are affected by shutdown. There may be some delays in processing if such operations are involved.
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