Actually, illegal entry into the US is indeed a crime, under the
Immigration and Nationality Act of 1952 (most recently amended in 2011):
Any alien who
1. enters or attempts to enter the United States at any time or place other than as designated by immigration officers, or
2. eludes examination or inspection by immigration officers, or
3. attempts to enter or obtains entry to the United States by a willfully false or misleading representation or the willful concealment of a material fact, shall, for the first commission of any such offense, be fined under title 18 or imprisoned not more than 6 months, or both, and, for a subsequent commission of any such offense, be fined under title 18, or imprisoned not more than 2 years, or both.