Obama helped put the law together, signed it into law, and has been warning about it since mid-2011.
The Republicans knew about it as well, and for most of the time they didn't want it either. However, they expected Romney to win the election, in which case they could modify the budget as they wished. And, let's face it, they've been throwing collective snits about Obama since January 19, 2009. Even before he was in office, Republicans were insisting they were going to kill his agenda and make him a one-term President.
When Obama was re-elected, they were forced to raise a handful of taxes on the wealthy in January. They continued their extended temper tantrum, and decided they'd rather deal with sequestration cuts than pass another tax hike.
In addition, Obama was saying as early as August 2011 that he wasn't going to modify the law and blunt its effect.
So I'd say that while everyone should have seen this far enough in advance to avoid it, no one (from either party) really expected it to happen until a few weeks before it actually hit. Nor is "insufficient notice" the fundamental problem.