The first thing to remember is the TSA are not officers of the law. This isn't my opinion, this is something making its way thought the senate at the moment:
"Rep. Marsha Blackburn (R-Tenn.), the lead sponsor of the Stop TSA's Reach in Policy (STRIP) Act, said that TSA has essentially allowed its airport screeners to play dress-up by giving them metal badges and police-like uniforms in recent years. But she said many airport screeners have no "officer" qualifications, and should have this title removed." source
They've had the ability to abuse rights, previously, because they've had you in confined situations where you've already had certain rights removed. The two most obvious examples being:
You'd like to get on that plane you've already paid a lot of money to travel on? Then, whether you like what we're doing or not, you have to pass through us to get to it. Plus, you've already entered in to a secure screening area. Declining our searches and simply choosing to leave means you violate the security protections and are subject to a $10,000 fine.
You're not on US soil. Until you've passed through customs, you're in magical land where we deny you're actually on US soil and as such have zero consititutional rights. We'd like your phone and laptop to take a copy of all data on it? You have no fourth amendment here, hand it over.
Yes, it's true that the government has basically torn up the constitution in the last few weeks. They can no detain anyone, forgeign or American, indefinitiely, without access to a lawyer, without charging them, without judicial review, just because they say that they're a terrorist threat. They do have a safeguard however: once a year, you're allowed to ask them if they'd like to keep doing it.
The thing is, big brother as that is, it's massively overkill for someone politely telling a TSA goon that the fourth amendment does still apply on the streets of the US and, unless they can provide a legitimate reason for your search and seizure, you will be polite but you will not comply with unreasonable requests from minimally trained screeners who, by the senate's own definition, don't have the qualifications or training to call themselves legitimate officers. If they disappeared every politely spoken person who passively resisted, their jails would rapidly fill and every news channel would run sensational headlines about it. The street goons are going to try to hype their authority a little, they'll most likely call a police officer over to back them up who does have a little more legitimate authority, but you're not going to end up in a secret prison.
So, my take? Stay very polite. Don't get heated. Don't get angry. Simply express that you recognize they are not law enforcement officers, they are essentially an extra type of security guard at this location and that you are happy to comply with reasonable requests that any other security guard makes. If they make unreasonable requests, you will simply leave that location. (If it's a venue, leave, write the management company about how their new security made for a hostile environment and how you'll be encouraging friends not to return until better training or their replacement is arranged - if it's a subway entrance, walk the extra couple of blocks and, again, contact the transportation authority and government to tell them how you were happy to abide by legal requests but their overstepping should not be allowed.)
Politeness, walking away, then slowly burying the decision makers with the weight of the bad decisions usually works far better than shouting and screaming, overstepping in to something you can legitimately get arrested for, then just making their point for them.
Also... The more people politely passively resisting, the harder the abuses become to maintain. I just spent the last week flying. At every scanner, I requested a pat down and was very polite about it. I also pointed out to everyone else in line that the scanner only has a 1:30,000,000 risk of killing you from cancer but terrorists only have a 1:60,000,000 risk of killing you on your flight so the TSA doubles your risk of death in order to save you. It really starts overloading them when everyone wants a pat down.