CU4, I am not sure that most people in the US are "conservative," but it doesn't really matter in class war terms, because their political leanings don't affect their class. By that, I mean that a person might be among the poorest of the poor and yet support a political POV that favours the rich against his own class. Regardless of his political position, he is still basically a poor man.
A "conservative" government with massive popular support would have to deal with its own contradictions. Their problem would be that while their basic ideology brought them support from the 1%, their base amongst the 99% would be demanding that their interests be served. The basic contradiction would be between serving the interests of the rich and of that portion of the 99% that supported them.
So the large popular support for conservative parties (GOP and Dem) is really a source of contradiction within both parties, since their real agenda is to serve the rich, but their more numerous supporters in the country will also be demanding service for their interests as well. Revolution will be violently suppressed as long as the parties in power have the support of enough of the 99% to get away with massive, up to lethal force against those who demand real changes, support which they apparently possess today.
However with the passage of time, the internal contradictions deepen and become harder and harder to explain away to the satisfaction of the 99%. Their continuing obligations to the rich prevent them from delivering on the real reforms which are demanded and routinely promised in vain. Support for the use of force ebbs, and the police and military units formerly counted upon to provide the muscle, begin to realize that they too are part of the 99%. Gradually, as the crisis worsens, the 1% can no longer count on the support of the majority of the country nor on the continuing loyalty of their goon squads. This point has not yet been reached, but it's definitely on the way.