You dont need outside support to declare independence, it is of no concern to those in Catalan what the US or anyone else thinks. The best course of action for the Catalan parliament would have been to call an election and then if they won it with a decent majority used that as their mandate to declare independence. As it is they dont have a solid mandate so it is easier for Spain and the EU to ignore them, however all those Catalans who didnt support independence may well change their minds if the spanish army comes rolling into Barcelona.
"You don't need outside support to declare independence" is a philosophically pleasing but politically unsound idea. It's the sort of thing that leads to martyred revolutionaries instead of redrawn boundaries on a map.
If a group of people had enough military might to declare themselves independent and not fall to subsequent invasion, then it doesn't matter what the rest of the world "thinks", they are independent.
They may be independent in some sense but it still matters a great deal. If other nations don't accept your sovereignty you can't really have trade or diplomatic relations. Just ask South Ossetia, Novorossia or Transdnistria. These days it's pretty pointless to be independent if you can't have foreign trade.
I'm pretty sure most sub-regions wouldn't trade their political dependence for North Korean-style independence (but I admit to not knowing the hearts and desires of most people ;) ).
Well, there's the Abkhazia option where you become a weird pseudo-state with no recognition. It's not great, even if you have a big friend like Russia who does recognize you.
By the same logic NYC can be independent of the NYS and the rest of the United States, which is ridiculous considering that it won't be able to withstand a week without food and fuel supplies from outside the five boroughs.