Let's imagine that you've been visiting the U.S. on a B-2 visitor visa, but things got messed up with flight connections and you have no choice but to fly back a day after your permitted U.S. stay runs out. Is this going to create problems when you try to come back to the United States in the future?
First, let's make sure you're looking at the right document regarding when you're supposed to leave the United States: Your visa is what you used to enter the U.S., and was stamped into your passport. The date it expires is NOT the date you must leave the U.S., but rather is the last date upon which you could use it to enter. (In fact, it might allow you multiple U.S. entries.)
To find the date by which you must actually leave the U.S., look to your I-94, which is either a small card placed into your passport by the Customs and Border Protection (CBP) official who met you at the U.S. airport, border, or other entry point; or, more likely, available online at the CBP website.
Now, assuming that your return flight is indeed one day after the expiration date on your I-94, let's consider the consequences. Most of these are indirect. Immigration authorities are highly unlikely to track you down over a one-day overstay. But the law can make your next visit to the U.S. more difficult.
Even an overstay of one day will result in your visa being automatically cancelled. So if you had a multiple entry B-2 visa, you are out of luck; it will no longer be valid for U.S. entry. (See Section 222(g) of the Immigration and Nationality Act (I.N.A.)
In the past, many foreign nationals who overstayed a U.S. visa took quick trips to U.S. consulates in Mexico or Canada, where they applied for another period of U.S. stay or a new visa.
Now, however, the law contains something called the consular shopping bar. It says that, after a visa overstay, only people who can show extraordinary circumstances can use a third country for a new visa application. The rest must go back to a U.S. embassy or consulate in their home country to apply for their next U.S. visa.
If your permitted stay in the United States hasn't yet run out, you are likely eligible to apply to U.S. Citizenship and Immigration Services (USCIS) for an extension of your stay. You'll do so by submitting USCIS Form I-539 and the required fee to USCIS before your I-94 expiration date.
Some, but not all applicants can submit this form to USCIS online. If you're among those who must submit by mail, be careful that it ARRIVES at the USCIS office before your lawful status expires.
Your stay in the United States becomes lawful as soon as that application is in. (But if USCIS denies the extension, you'll have to leave the U.S. right away.)
If you've already left the U.S. by the time you read this, and didn't apply for an extension, your one-day overstay does not bar you from future visits to the United States. (You would have had to overstay by at least 180 days to become inadmissible.)
But the overstay could make it harder to convince a consular official to give you a visa in the future. Whether to approve you for a visa is, after all, fully within their power and discretion.
Along with the other required materials to apply for a B-2 visa, you'll want to bring proof of the complications that led to your overstay to your consular interview, and be ready to explain that you had intended to leave on time but were prevented by circumstances beyond your control.
Whatever you do, don't attempt to conceal the past overstay. If the U.S. government finds that you misrepresented the facts, it will deem you inadmissible on that basis.