I think that most conservatives believe that the federal government should function in strict adherence to the US Constitution.
Regardless of what the president thinks about the immigration laws, it is not up to him to decide which laws his administration will enforce and which to ignore. When he took the oath of office, he swore to faithfully execute all of the laws passed by the US Congress. To willfully ignore to enforce any law breaks that oath. Only the US Congress can change the law. He must work with Congress if he wants changes. Declaring to not deport certain illegal immigrants and issuing them work permits is probably unconstitutional.
Advocating that presidents should break their oath of office and refuse to enforce any law that they dont like would just invite chaos and anarchy. Endless impeachment proceedings, petitions to the SCOTUS to intervene. Thats no way for a great country to run a government.
I believe the founding fathers got it right. Let the laws be written by the peoples representatives in Congress, and then have those laws enforced to the best ability of the president as sworn when taking office.
True only for laws that are constitutional. If the president believes that some law the Congress has passed is unconstitutional, then, in order to keep his own sacred, binding oath to support the Constitution, he has an obligation to provide the appropriate check and balance on the other branch.
In this case, there is no shadow of any doubt whatsoever that Congress, in Article 1, Section 8, possesses the sole grant of constitutional power to govern immigration and naturalization.