Doesn't having a rogue despot in the White House bother them in the least?
I-M-P-E-A-C-H-M-E-N-T
Yep, it’s not constitutional, since this is Congress’ domain
“The Supreme Court has ruled that the Congressional power to regulate naturalization, from Article 1, Section 8, includes the power to regulate immigration (see, for example, Hampton v. Mow Sun Wong, 426 U.S. 88 [1976]).”
http://www.usconstitution.net/constnot.html#immigration