I can only speak for my own low cost airline (easyJet in the UK) and say that whatever criticisms may be brought against their managment, when it comes to safety there are absolutely no shortcuts being taken. They have brand new aircraft and have excellent maintainance practices. I have never once been asked to carry a snag that should have been sorted and I know of no one within the company who has been asked to do so either. Quite the contrary - my worry would be more making an error that is spotted by the 'spy in the cab' recorders then being called up to head office to account for it. Companies like easyJet know that however expensive safety is, a crash is a whole lot more costly! There is an huge emphasis on adherence to SOPs within a company like ours and as long as you make a safe decision in a situation the company backs you 100%. For example, if you do a go-around for being unstable at 500' you will never hear a word about it because it was safe. If, however, you continue the approach you will certainly hear a lot about it! I personally feel at ease in working in that sort of atmosphere and it is one of the plus points of working for easyJet.
You could take the above commentary, replace "easyJet" with "jetBlue", and it would be spot on.
I do not see "minimum levels of maintenance", as you say, being carried out at my company. Nor, do I see it at other LCCs in the U.S. (according to my friends at those companies).
At jetBlue, Safety is the first "value" -- I know it sounds cliche, but it really is true, at least from my perspective. It's even the official corporate position.
That's my opinion of the LCC situation, at least in my country.