Direct opposites:
* Push away: This is the most literal opposite, meaning to move something or someone away from you.
* Repel: To push back or ward off.
* Discourage: To make someone less likely to do something.
* Deter: To prevent someone from doing something.
Other contrasting actions:
* Ignore: To pay no attention to something.
* Dismiss: To reject or disregard.
* Overlook: To fail to notice something.
* Obstruct: To block or hinder something.
* Oppose: To disagree with or resist something.
Words suggesting firmness:
* Command: To give a direct order.
* Insist: To demand something firmly.
* Force: To use power to make someone do something.
The best antonym for "nudge" will depend on the specific context of the sentence and the intended meaning.