1) even if the GOP has the best possible outcome in Nov, it will be several votes short of 60, let alone 67 needed to convict. That number is just not remotely achievable.
2) it is still possible for Dems to hold the Senate. Not likely, but possible.
3) a radical development such as an impeachment in the House or a pre-election shutdown of government could hand the House to the Dems. Not likely, but possible.
From the Republicans' point of view, IF OBAMA FLAGRANTLY VIOLATES THE LAW they have no power. If the House does shut down the government, do you think Zero will stop spending? Stop implementing Obamacare? Suddenly not do a climate "deal"?
Rush is going over this now, but even he isn't going to the logical extreme: if you have a corrupt lawless thug in power, and the "honor system" is gone, whereby the executive plays by the rules, then it's a new game and it doesn't matter what the GOP does, majority or not.
This is why Romney---for all his faults---was so important: he still believed in playing by the rules and the honor system.
By your argument, the GOP has nothing to lose in cutting off appropriations to El Presidente.