If Congress turns off sequestration in a way President Obama supports, it will be because of a slow attrition of rank and file Republican support, and my guess is it will require Obama to make sacrifices he never expected to have to make.
This was all predictable enough in hindsight. But it's worth remembering that there were two prevailing schools of thoughts among Democrats and their allies during the fiscal cliff fight. One was that Democrats should pocket some revenue and fight sequestration separately (which is what ultimately happened); the other was that Obama should allow the GOP to take the country over the cliff, then work backwards -- use the allure of tax cuts to win buy in from Republicans to turn off sequestration.
There were decent arguments at the time for both strategies. The White House chose the former and attempted to convince advocates of the latter that their approach was too risky. But those people, including Democratic leaders in Congress, appear to have had it right the first time around.