I came to the U.S. on a K-1 fiance visa. We got married and everything, but it's been taking a long time to get the paperwork together for the adjustment of status packet. For one thing, it took weeks to get the official marriage certificate. My spouse's employer took its time about providing a job letter, too. I just looked at my I-94 and realized it has expired. Now what do I do?
Don't panic, but definitely act quickly. Your status in the U.S. is currently unlawful, meaning that if you were, for some reason, encountered by U.S. immigration authorities, you would be placed into removal (deportation) proceedings. But that is not the most likely scenario.
More likely, you will still be able to submit your adjustment of status packet (by mail). Assuming it's based on your marriage to the same person who petitioned for you to receive the K-1 visa, U.S. Citizenship and Immigration Services (USCIS) will accept it for processing.
The key thing at this point, however, is that your proof of having been approved for a K-1 visa can no longer serve as the basis of your application. In its place, your U.S. spouse will now have to fill out an additional form for you, called a visa petition, on Form I-130. What's more, you will have to pay the fee associated with Form I-130 (which you can find on its page on the USCIS website.)
If it does happen that you are picked up by Immigration and Customs Enforcement (ICE), this isn't the end of the world either. You will (unless you fall into a rare exception, such as having a previous deportation on your record), be given a "Notice to Appear" and a date to go to immigration court, for removal proceedings. There, you can present your application for a marriage-based green card to the immigration judge.
The downside of having your case end up in court is that you will probably have to spend thousands of dollars in attorney's fees. Plus, the judge will be legally bound to give much stricter scrutiny to the bona fides of your marriage than USCIS would have. Nevertheless, if you can explain what went wrong, and convince the judge that you and your spouse truly intend to establish a life together in the U.S. (and aren't just committing a fraud to get you a green card), the judge should approve you for the green card at the end of your merits hearing.