I don't remember Congress actually giving them money.
What happened was Congress said: stop screwing around and use the money we have already budgeted for you, but you refuse to use.
The FAA intentionally furloughed operational controllers, instead of suspending development projects and other activities that weren't needed during that time.
In other words, they threw a fit.
Not exactly.
The FAA, like any government agency, has certain accounts to spend money on things. When I worked in Washington DC and the Pentagon, we referred to these a "colors" of money. Some are for procurement, some Operations and Maintenance, some for Overseas Contingency Operations (wars), etc.
http://www.cnn.com/2013/05/02/travel/faa-furlough/
After 40,000 flights were delayed and 1,900 cancelled in just the first few days, Congress moved very, very, very quickly to "re-program" money so it could be used for salaries.
President Obama had to sign it.
Sequestration was used as a political game, with many employees being used as pawns. The DoD took a huge hit in funds, midway through the Fiscal Year, and said that was why they had to furlough so many. But, Hagel played political games with it. He "exempted" politically correct "sexual assault" briefers who had been on the job only 2 weeks. The propaganda that every member of the military was a sexual rapist was going strong at that point in 2013. The truth was, these PC priestesses were doing nothing of value for the military. Hagel also exempted Navy shipyard workers, because he and Obama could not stand the blow back from their union, and the "optics" looked really ugly.
But those Sequestration furloughs (that were never paid back) devastated the DoD and some other agencies.
That had horrible effects that military and military families are still dealing with.
In the meantime, since 2013, we have paid out almost 1 Trillion in "benefits" to illegal invaders. This was a political game, and real people were caught in the cross hairs.