They lose
their base of support.
If they are incurably foolish they will continue to listen to the liberals who will explain that their low support ratings are because "they sold out to the ultra right wing".
There's only one President who steamrolled to two landslide victories, and he was
no RINO. The icing on the cake was his wholesale capture of conservative Democrats. You can do that by catering to the whims of the left. Even Obama can't do it!
I guess we'll just have to keep voting the RINOs out of office and replace them with Republicans who understand what it is to be an advocate for freedom and liberty, not socialism and bigger government.