To eat crow American to-infinitive
If someone eats crow, they admit that they have been wrong and apologize, especially in situations where this is humiliating or embarrassing for them.
I have to eat crow for my false assumptions to Peter.
I told with the whole class that I'm going to win the debate competition. If I don't win, I will have to eat crow.
Thinking Steve stole her wallet makes Liza eat crow.
The phrase starts with a verb, therefore, it needs to conjugate within the sentence.
According to the research of Word Histories, to eat crow first appeared in 1850 in a story the Buffalo Daily Courier (Buffalo, New York) and became so popular for over two decades.

To encounter bad luck, or being picked doing something undesirable
Mike drew the short straw and had to clean the bathroom