The underlying concept of the TP, as it exists today, is anti-liberal. With a Dem in power that means anti-everything from taxes to social policy. If the TP survives until the GOP is in power, it will become strictly social policy, since they will not challenge a right wing government, and social policy is the right's evergreen gripe via convenient scapegoats like the courts, the media, Hollywood, universities, the "elite," yadda yadda.
Now all this could change if a Paulite captures (the correct word might be recaptures, since some of the TP genealogy dates back to the Ron Paul Experience) the movement, in which case they could retain their message and energy even against a GOP establishment.
But right now it's still very much the handmaid of the Republicans and the GOP is using them. They won't be truly what you seem to want to think they are unless they start protesting GOP spending priorities under a GOP administration.