He was never offered "President for Life," at least as far as I know. In fact, there are too many things fundamentally wrong with such a notion for it to have even been possible. Firstly, to do such a thing would be to totally undermine the fledgling Constitution and prove the arguments of Madison and Jefferson to be true. Secondly, the Constitution placed no limit. Nothing really stood in his way if he wanted to be President for the rest of his days as it was. He might have a tougher time getting elected, but he probably could have been elected at least one more time, which would have made him President until his death in 1799. Maybe it was proposed by some more radical Federalists or perhaps in personal correspondence, but it was certainly never offered in any official capacity.
To further back up my point, here is an excerpt from James Flexner's biography of Washington:
"Rather than stilling public controversy as he had hoped, his ratification of the Jay Treaty had turned the anger on himself. The broad public, which had previously resented attacks on their hero, now accepted them with avidity. Every aspect of his career was discussed insultingly in the newspapers. He had been made commander in chief because he was such a nonentity that Congress was convinced that he could not become a tyrant--but how wrong Congress had been! Even the infirmities of old age were used to blast at him. Why did he not walk around or ride horseback as he used to do? That he only passed through the streets in his well-appointed carriage surely expressed anti-Republican disdain."
