The Tea Party's main platform was "GAH OMG TAXES!!" That in itself is fine, except when you destroy everything in the process. At heart there was nothing new but the name, stolen from some Ayn Rand libertarians, and a lot of questionably-used campaign contributions.
Otherwise it was just the same GOP base red meat in party form. Other than a name that refs an event that occurred the same century it was written, there's nothing especially Constitutional about the Tea Party's stated goals (the Boston version would have still been illegal under the Constitution, and those kinds of tariffs are things the Trump administration has supported and proposed). The burden would be on any current or past tea party members to explain just what part of the document they were recognizing. Like Article and Section. Eg., Trump is in violation of Article 1 section 9 (and yet none have come forth to denounce him.)
Some people at the time, I guess, were told that a common market for buying health insurance and extending Medicaid to people my age, was socialism. The Constitution doesn't say anything about it, therefore the ACA is a total destruction of it, and the black President was a Tyrant like we knew all along.
Sadly, the Tea Party never managed to become a party of its own, and maintained its Republican registrants. That worked out occasionally with primary challenges screwing up established GOP politicians, but pushed the incumbents further to the right; instead of flipping a lot of seats, it landed a few of them the actual election.
Now, frothing rage is usually not a good place to choose your reps from, and the guys (of course it was white guys) who went in had a short vocabulary--NO, and if Obama had anything to do with it, FUCK NO.
Certainly they were seen and heard; i'd say too much of both, and plenty wound up in Congress, where they supported the Constitution by shutting down the government. Those are the ones Boehner had to deal with. Things are much more quiet and confused among them today, as they find they have a constituency that now realizes it was bamboozled on the Replace part, of the Repeal of the ACA. And that certain parts of it are kind of swell. Soon the chants, instead of "government out of my Medicare!" may be, "government out of my Obamacare!"