4th amendment.You're probably thinking of 5th Amendment protection against self-incrimination.
They can sue, but they won't win. SCOTUS has ruled that when you fly, you are waiving a lot of rights. For example, having Customs and the TSA going through your bags without a warrant. Or, agreeing to breathalyzer or field sobriety tests as a condition to getting a driver's license. What they've announced is that getting on a plane to NY constitutes waiving your rights. Don't want to be questioned? Don't get on a plane to NY.
Unlawful search and seizures are protected by this amendment.
Forcing people off an airplane or driving into your state from certain states with out of state plates to be subject to stops is a violation of the 4th amendment.