Congratulations on your marriage! Since you are married to a U.S. citizen, and applying for Adjustment of Status, your being out of status would not be a bar to Adjustment. That means, even if you were to go out of status when your documents are filed, you will still be able to adjust your status. To be eligible for Adjustment of Status, you have to show that you entered the U.S. with inspection (in your case you entered with a J1 visa), and that you are married to a U.S. citizen. So even if you were out of status for a year or more, you would still be eligible for Adjustment. However, in your question you did not mention whether your J-1 visa has a two-year home residency requirement. If your J-1 visa requires two-year home residency, then you must get a waiver of that requirement before you can adjust your status.
Answered on Sep 30th, 2013 at 11:37 AM