"Republicans" do, but not conservatives. Then you have Rand Paul and a handful more who are way to the right, are Libertarian really, and are not willing to compromise their principles to work with the "moderate Republicans." This is really manifesting itself in the healthcare debate.
I don't particularly like Mitch McConnell, I think he is TOO MODERATE, but you are misinformed if you think he is not a good leader in the Senate. He is, in fact, exactly what the Founding Fathers envisioned for a majority leader in the Senate. He is the polar opposite of Dirty Harry who routinely violated Senate rules and traditions to hammer home his socialist agenda. Many on the right (including Trump) want McConnell to do the same thing.