One refrain I often hear is the Republicans do not have an alternative to present. Paul Ryan has one, but how much you want to bet that Nancy Pelosi is going to let him present that bill? Come on, know a bit how the game works (and yes we hear these same whines vs. the Dems when they were out of power in the House) and it is when you are in power you use it for all you are worth, as well all know, it is easier to ask for forgiveness than permission.
So, what are the Republicans to do? It would be silly to attempt to pursue their own agenda at the moment, because the leadership in the Congress & the Whitehouse will not allow it. The Republicans have one objective and that is to stop the Dems from getting everything they want and to not cooperate (as much as possible) in passing damaging legislation. The Democrats can pass whatever they want, let them own their bills, let them take credit for the misery their bills bring.
When I'm driving from time to time I find the car going in a bad direction. Young drivers tend to overreact and put themselves into another bad position (or flip their car). The first goal of getting out of your predicament is to stop your current situation from getting worse, once that is done, then correct direction.
Republicans must first stop the Democrats and then can work on getting their wheels out of the ditch.