He could take over games almost singlehandedly. He was a truly great player.
To Cowboys fans who never saw Staubach play:
No analogy is perfect, but if you want to get a feel for who and how Staubach was as a player, think of Michael Jordan. Not the young flashy Michael Jordan, but the more mature Jordan who was winning championships.
Staubach and Jordan both displayed remarkable and very rare levels of focus, determination, and competitiveness. They both showed a unique ability to deliver in the clutch. It was as if they could use their own intensity to will their teams to victories. Teammates had unquestioned faith in the ability of Staubach/Jordan to win games in the closing moments.
Players on opposing teams often knew that they were no match for Staubach/Jordan. You'd often see opposing teams deflate in the closing moments of games, as if they were preparing themselves to be humbled by Staubach/Jordan. Staubach and Jordan were true masters of their game.
At the heights of their careers, both were seen as the best player of their sport and were the single most famous player of their sport. Both were unusually popular.