if you raise the lead to something meaningful like 5 or 6, it would be tough to fold to a 3bet push, so i see why you're saying push or fold. but im not sure enough worse hands call a massive overbet push (maybe top pair?). if he's calling that with mid pairs or draws then go for it. tough hand, but i think id call and push/fold the turn depending on bet size and post flop reads (does he fast or slow play monsters, fast play draws, fast play marginals with draws out, etc)