Actually it's not.
While it is illegal to sneak across the border or overstay a visa, there is NO LAW ANYWHERE that says staying in this country is a crime, afterwards.
That is WHY the House was trying to pass a law making it a felony. Presently it is not a crime under our laws.
Really?
U.S. Code
TITLE 8
CHAPTER 12
SUBCHAPTER I
§ 1101. Definitions
(a) As used in this chapter—
(3) The term “alien” means any person not a citizen or national of the United States.
SUBCHAPTER II—IMMIGRATION
Part VII—Registration of Aliens
§ 1302. Registration of aliens
(a) It shall be the duty of every alien now or hereafter in the United States, who
(1) is fourteen years of age or older,
(2) has not been registered and fingerprinted under section 1201 (b) of this title or section 30 or 31 of the Alien Registration Act, 1940, and
(3) remains in the United States for thirty days or longer, to apply for registration and to be fingerprinted before the expiration of such thirty days.
(b) It shall be the duty of every parent or legal guardian of any alien now or hereafter in the United States, who
(1) is less than fourteen years of age,
(2) has not been registered under section 1201 (b) of this title or section 30 or 31 of the Alien Registration Act, 1940, and
(3) remains in the United States for thirty days or longer, to apply for the registration of such alien before the expiration of such thirty days. Whenever any alien attains his fourteenth birthday in the United States he shall, within thirty days thereafter, apply in person for registration and to be fingerprinted.
(c) The Attorney General may, in his discretion and on the basis of reciprocity pursuant to such regulations as he may prescribe, waive the requirement of fingerprinting specified in subsections (a) and (b) of this section in the case of any nonimmigrant.
§ 1306. Penalties
(a) Willful failure to register
Any alien required to apply for registration and to be fingerprinted in the United States who willfully fails or refuses to make such application or to be fingerprinted, and any parent or legal guardian required to apply for the registration of any alien who willfully fails or refuses to file application for the registration of such alien shall be guilty of a misdemeanor and shall, upon conviction thereof, be fined not to exceed $1,000 or be imprisoned not more than six months, or both.