Team A has the ball on Team B's 1 yard line. A1 takes the handoff and runs into the line but his forward progress is stopped by Team B before crossing the goal line. A2 comes behind A1 and provides extra force by pushing A1 into the end zone. The call on the field was touchdown! Good call or bad call?

Bad call. Bad no-call.

First, you state that the runner's forward progress was stopped. Dead ball at the spot.

The runner (because of that no-call) carried a live ball into his opponents end zone. Touchdown.

But wait! The runner was pushed from behind by a teammate. Rule 9, Section 1 HELPING THE RUNNER. 5 yards from the spot of the foul.

Defense gets the option of enforcing the penalty or taking the result of the play. Replay the down from the six or touchdown. The choice is obvious.

Oh, another no-call you say?! No flag on the "Helping"? Bad, bad. This one gets missed a lot.

Touchdown stands.

Too bad.

Sometimes, this is an obvious call, as one kid will plant both hands in the back of the runner and push. That's easy. The hard one is when there is this mass of humanity and the big uglys from A slam in to the back side of their side of the pile - not so obvious, but the intent is clear - move the pile. The coach from A is screaming during the play, "Move the pile!" so they do it.

If they get right behind the runner and push, it's a foul. There's a lot of gray area here, though. It's got to be clear for me to throw it.

I agree its a tough call to make.
 

I've only called it once in 9 years of officiating.

Its an easy call, usually for the referee because he will be trailing the play, if the offensive player actually puts his hands on the back of the runner and pushes him forward.

As you note, the usual case is that there is a mass of players surrounding the ball carrier and normally you will have an offensive player continuing his block on the defender and the runner just happens to be in the way.

Actually, I've had several fouls by the offense for blockers coming into the group of players late and blocking a defender in the back or a personal foul. And of course there is the runner being held up by one or more tacklers and the next tackler drives his helmet into him, etc.

So assisting the runner is one of many fouls we need to be alert for.

play dead
 

why didn't the linesmen or linejudge blow the play down if his forward progress was stopped?

NO TOUCHDOWN

As a LJ, I can tell you that I can't always see the forward progress of a runner, especially in a goalline situation where there's a huge mass of humanity between me and the runner. I also can't see if a lineman is pushing the running or just pushing the pile. That's you're call.