The action does not have much chance of success. President Obama has the authority to grant reprieves and pardons for offenses against the United States under Article II, Section 2 of the Constitution; which would extend to a grant of amnesty for unlawful entry into the country. The President's power to grant pardon and reprieves may be made conditionally or absolutely; and Congress cannot limit the President's grant of an amnesty or pardon.
United States v. Klein, 80 U.S. 128 (1871). And, there is plenty of precedent for granting amnesty by executive order:
http://www.pensitoreview.com/2014/11...an-presidents/