Huber is right, conservatives can win and have won and will in the future win in Democrat-leaning districts.
If your "majority" is provided by liberals (oops, "centrists"), what do you expect to accomplish?? Not much, and eventually the voters will get tired of your nothingness and toss you out on the street with little to show for your years in the "majority".
That goes for both RINOs and 'conservative' reps who become fat, complacent, and tone-deaf.
"...If your "majority" is provided by liberals (oops, "centrists").."
Historically, and in strictest political terms, Republicans ARE Liberals. Look it up, you might learn something about Classical Liberalism, and if you do, please tell your friends.
What we refer to as "liberals" are nothing of the sort. Unless, of course, you consider government-supplied-and-controlled-everything-intruding-into-every-nook-and-cranny-of-your-life to somehow be a liberal ideal. If anything, they are certainly not liberal (if we use the word correctly), and what I think you mean to say (if you'll allow me) is "libertine", with regards to their social views.