What happens if a passenger wants to get off the plane during a runway delay because it ruins their travel plans completely

(From your mention of FAA I assume you are interested in the United States. Rules in other parts of the world may be different.)

Yes, the US Transportation Department has specific regulations for "tarmac delays" at 14 CFR 259.4, as well as an informal summary for travelers.

The general rule is:

[14 CFR 259.4 (c)(1)] For all domestic flights, each covered U.S. air carrier shall provide a passenger on a flight experiencing a tarmac delay at a U.S. airport the opportunity to deplane before the tarmac delay exceeds three hours in duration, subject to the exceptions in paragraph (c)(3) of this section.

For international flights, the limit is four hours instead. There are exceptions in case deplaning would be unsafe, or would significantly disrupt airport operations. There is also a technicality that they only have to begin the process of returning to the gate before the three-hour mark, and it's okay if it takes longer before they actually get to the gate and can start deplaning.

Airlines could of course make their own policies promising to return to the gate sooner, but as far as I know, none of them have.

So in your example, you are out of luck. If the delay has only been 1.5 hours, the airline is not yet under any obligation to take the plane back to the gate so you can get off.

(It should go without saying that you should not attempt to get off of your own accord, e.g. via emergency exits, nor to force a return to the gate by causing a disturbance, threatening violence, or anything like that. Those are federal crimes.)

If the flight should manage to take off within a further 1.5 hours, you will just have to go along with it, even though it ends you up somewhere that you no longer want to go.

In future, plan your itinerary accordingly.

It's not going to happen.

You cannot exit the plane without it going back to the gate. It's unsafe. The crew will refuse to let you. If you continue to try they will probably restrain you and you will be in other trouble.

The plane will not return to the gate for you to disembark just because you have decided you want to. Doing so will delay the plane further, possibly much further, and inconvenience all the other hundreds of passengers on the plane.

If you attempt to exit the plane after being told not to, or otherwise disrupt the flight, you will compromising the safety of the plane. The probability is that the plane will return to the gate, where you will be arrested, as well as delaying the plane more and causing you to be very unpopular with other passengers. The punishment you receive will be significant, and part of it will probably be that you will not fly again for a long time.

For a long enough delay the plane will return to the gate to let you disembark, but I believe the norm is 3 or 4 hours.

You should be able to obtain some compensation for the delay, depending on circumstances and jurisdiction. Assuming you haven't tried to force your way off the plane.

I once flew London to New York; flight diverted to Boston because of bad weather and stayed on the tarmac for 3 hours; a family who asked to leave the plane at Boston were firmly told this was not allowed. Eventually the crew ran out of flying hours and all the passengers were disembarked; the family were still told they had to continue their flight for immigration reasons, but they absconded.

There is no longer any reason for me to travel and even though I can't get my money back (sunk cost). At this point, getting off the plane is a no-brainer for me.

Think of air travel as a group project in school. Just because you no longer have an interest in biology (being on the plane) does not mean you get to ruin it for others.

When a plane is delayed it has to wait diligently (up to 3 hours) for the ATC to clear them for take-off. This window of opportunity is small so the plane must be ready to go at all times.

Short of a medical emergency, if you were to miraculously convince the crew to go back to the gate and the plane gets cleared for takeoff while you're deboarding then you will make a lot of silent (sometimes loud) enemies because now they have to wait for clearance again.

If the flight crew times out then they have to wait for another crew; sometimes from an incoming flight.

If people are making international connections it is imperative to at least get them one step closer to their destination. If you're in a small city and destined for a big city then think about how much more likely the other people can connect to their final destination.

As for compensation, read your airlines' ToS. It's usually SOL for weather delay but you could request a full refund for mechanical issues.

Better yet, get travel insurance next time.