You can't pay more life than you have, even if you won't lose the game.

If you control Herald of Eternal Dawn in a Two-Headed Giant game, your team can't lose the game and the opposing team can't win the game.

No game effect can cause you to lose the game or cause any opponent to win the game while you control Herald of Eternal Dawn. It doesn't matter whether you have 0 or less life, you're forced to draw a card while your library is empty, you have ten or more poison counters, you have no other choice out of your Demonic Pact, an opponent reaches the Maze's End, or so on. You keep playing.  

Other circumstances can still cause you to lose the game. For example, you will lose a game if you concede or if you're penalized with a Game Loss or a Match Loss during a sanctioned tournament due to a tournament rules infraction.