Republicans would like to see the Federal Government run in accordance with the U.S. Constitution. They would like to see the government run in accordance with the law (e.g., immigration laws).
Just for fun, you Leftists out there, name a single Democrat initiative - going back to FDR if you must - that is not unconstitutional. Let me give you a few to chew on;
Social security (unconstitutional)
Welfare (unconstitutional)
Housing subsidies (unconstitutional)
Obamacare (Unconstitutional)
Gay marriage (unconstitutional)
affirmative action (unconstitutional)
The "right" to abortion (unconstitutional)
The "right" to bugger your neighbor (unconstitutional)
You get the idea. Name one Leftist initiative that is not unconstitutional. Be prepared to defend your position.