They need the rest.
Utah has outworked the Spurs in all 3 games of this series. In games 1 and 2, we ran up a 17-18 pt lead and did enough in the 2nd half to prevent the Jazz from catching up. In game 3, we had a small lead in the 1st half and got blown away in the 2nd.
It might be that the Jazz's relative youth and energy levels have been too much for the Spurs to handle later in the game.
Or it might be that the Spurs haven't really had a typical 2nd half in this series. Games 1 and 2: they didn't have to do too much. Game 3: foul trouble limited Duncan, Bowen and Oberto's contribution. I want to see a 2nd half where there's lots to play for, and everyone gets enough minutes before commenting on the Spurs' late-game woes.
In either case, the Spurs need the rest more than the Jazz do