Nobody can task you to do a bad job. You do that yourself. You may find excuses for doing a bad job, but you chose to do it, they didn't hold a gun to your head.
If I find that I absolutely have to either cut corners or let the deadline slip, I let the deadline slip. I refuse to knowingly release crappy work, you can fire me for it, I don't care. But long before that deadline, I will have explored the options for changing the scope of the project so such a decision isn't necessary.
"Just find another job" isn't sufficient because every job involves making tradeoffs between personal goals and business goals. I believe in being real clear with management about what's happening so that we can work towards an equitable solution.
In this case, no you can't. Company politics has placed a superior of yours explicitly tasked into order you to do a bad job.
I do completely agree with the "just find another job" line. What I don't agree is with that "cheer, your job is less stressing now".