From the piece:
No matter who first came up with the idea, it took bipartisan votes to make it a reality. In other words, the sequester was part of a negotiation in which the two sides were haggling over an enforcement trigger that would cause pain on both sides. We examined this question when we awarded Two Pinocchios to the Mitt Romney campaign for trying to blame the defense cuts contained in the sequester only on President Obama.
As noted above, the Obama administration originally wanted the trigger to hinge on repeal of Bush tax cuts on the wealthy. Republicans responded by saying the trigger should be balanced by repeal of the individual mandate in Obama’s health-care law.
Ultimately, that was too much for both sides, so they settled on security spending (pain for Republicans) balanced by nonsecurity spending (pain for Democrats). But the fact remains that both sides agreed to take this step together.
In other words, Republicans cannot hide from the consequences of their own actions, especially because at the time they crowed that they had won a great victory.