McGonigal justifies this claim by reference to a single study: (Keller et al. 2012).
McGonigal says:
they started by asking people, "How much stress have you experienced in the last year?"
This is basically true. The study asked "During the past 12 months, would you say that you experienced a lot of stress, a moderate amount of stress, relatively little stress, or almost no stress at all?"
McGonigal says:
They also asked, "Do you believe that stress is harmful for your health?"
This is false. The study asked "During the past 12 months, how much effect has stress had on your health—a lot, some, hardly any, or none?"
This is significant in that the study was looking at whether people believed that stress had already started to affect their health, not whether the person had a nebulous belief about whether stress is harmful for health.
It is reasonable to expect that people who have already noticed health effects due to stress will die sooner.
The paper muses for some time about the possible forward causation between belief in the effect of stress and poor health outcomes before admitting (emphasis mine):
Adults who reported poor health may have been more likely to report that stress impacts their health simply because of their poor health status; moreover poor health status could also have influenced the amount of stress reported. The cross-sectional nature of these data precludes us from examining the direction of causality among the amount of stress, the perception that stress affects health, and health outcomes.
Summary
McGonigal used a single study to support this claim. That study didn't ask the question of its participants that she said it asked. It wasn't designed to be able to find a causation from "belief that stress is harmful for your health" (McGonigal's words) to "poor health outcomes". It wasn't designed to be able to find causation from "how much effect has stress had on your health" (authors' words) to "poor health outcomes". The study didn't claim any findings of causation, either.
References
Keller A, Litzelman K, Witt W, et al. Does the perception that stress affects health matter? The association with health and mortality. Health Psychology [serial online]. September 2012;31(5):677-684. Available from: PsycARTICLES, Ipswich, MA. Accessed February 12, 2014