Screening at the gate (for domestic flights) is very rare and the majority of it is ID checks. I've also seen checking of carry-ons. I've never seen any pat-downs at gates any time recently. And I've had very long connecting times at DFW and spend most of it walking through the terminal. That doesn't mean it never happens, but means the chances of it happening to you are extraordinarily low.

As to what happens if you decline, signs say that you won't be allowed to fly: I doubt that it would go further than that because the legal basis for more in that situation is far shakier than declining follow-on searches at the checkpoing.