No. If the Department of Homeland Security, Customs and Border Protection Immigration Officer at the port of entry (generally an airport) admitted you into the United States for a specific period of time, s/he will note your authorized period of stay on your I-94 card, called an Arrival Departure Record. You will be able to remain in the United States during your authorized period of stay, even if your visa expires during the time you are in the United States. Since Form I-94 documents your authorized stay and is the official record of your permission to be in this country, it is very important to keep it inside your passport.