As Karl pointed out, when Congress was debating the Budget Control Act in August of 2011, Ryan supported the framework and urged his fellow Republicans to vote for the sequester:

KARL: Congressman, I’ve heard you Republicans for a long time. This was the president’s idea on and on and on but let’s look at your own words. What you said right after the law putting this in place was passed in August of 2011. These are your words. You said “what conservatives like me have been fighting for for years are statutory caps on spending, literally legal caps in law that says government agencies cannot spend over a set amount of money and if they breach that amount across the board sequester comes in to cut that spending. You can’t turn it out without a supermajority. We got that into law.” Now, it sounds to me there like if you weren’t taking credit for the idea of the sequester, you were certainly suggesting it was a good idea.

RYAN: So those are the budget caps on discretionary spending. Those occurred. We want those. Everybody wants budget caps. The sequester that we’re talking about now is backing up the super committee. Remember the Super Committee in addition to those caps was supposed to come up with 1.2 trillion in savings. The Republicans on the super committee offered even higher revenues in exchange for spending cuts as part of that. It was rejected by the president and the Democrats. So no resolution occurred and therefore the sequester is occurring.