Let us first stipulate that the GOP is both competent only in its collaboration with the Progressive agenda, and incompetent as the putative opposition party to same.
If the GOP were intending to advance the American cause (a/k/a conservatism), it would respond to B. Hussein Obama's sequester lies and demagoguery thus (via officeholder message discipline, and running paid TV ads to bypass the Progressive Media censorship):
As head of the executive branch, President Obama has wide discretion in choosing where and how to make the budget adjustments required under sequester. He has signaled his intention to utilize "executive action" to furlough air traffic controllers and disrupt air travel; cancel Navy deployments to the Persian Gulf, even as Iran grows ever closer to having a nuclear weapon; and releasing criminals from detention and setting them loose in our neighborhoods.
He could instead have used his "executive action" power to leave those critical items untouched, and instead cut the following, which he has left untouched, and so apparently considers a higher priority than our military, air traffic control, or your family's security in your own neighborhood [then cite frivolous / infuriating budget items that were spared].
Alas, the GOP won't do this, or anything like it. As usual ...