Unfortunately, unlike in some visa categories, you cannot pay extra in order to receive faster ( premium ) processing of a K-1 visa petition. The U.S. embassy or consulate is likely to take 2 to 3 months to process the visa, depending upon the number of other visa applicants it's dealing with.he citizen will also need to pay the visa petition fee. Once the petition is submitted, USCIS will review it for completeness. Assuming the citizen didn't forget to include something, he or she will, within a few weeks, receive a Form I-797 Notice of Action acknowledging receipt of the petition.