I'm not an H1-B, but I am on a skilled migrant visa in a different country. While I'm not constantly thinking about it, I'm keenly aware that my immigration status is directly tied to my job. No job, no residence permit. So at a minimum I would say I have an incentive to not get fired, and the best way to not get fired is to be someone worth retaining.
Most Americans are motivated to not get fired also as that means you lose your health insurance, group life policy, and ability to pay your mortgage or rent.
