I’m assuming for purposes of discussion here that your spouse is living in your marital home and has agreed to leave but now doesn’t seem to be moving or making any plans to move. Let’s break this down to a series of “ifs:”
If you have a binding agreement specifying a date certain for your spouse to vacate the house and a judge has incorporated that agreement into a decree, that means you don’t just have a contract; you have an order from a judge instructing your spouse to move. And that means that, unless your spouse can show he is unable to comply, he is in contempt of the court. In most states, that means the judge may not only order him to comply immediately but also assess him for your attorney fee for forcing his compliance. That’s a powerful hammer you can threaten to use without actually using (as in a polite matter-of-fact conversation with your spouse) and make it clear your spouse has all the incentive he needs to get moving. Pronto.
If you have a binding agreement that’s not yet incorporated into a decree, it’s good to have but much less useful for forcing compliance. In order to force compliance, you would need either to incorporate the agreement into a decree so you can have the leverage described in the preceding paragraph, or resort to suing your spouse to force compliance on your own.
If all you have is an informal assurance from your spouse that she’ll be gone by a date certain, even if that assurance is in writing, your spouse has failed to comply with a moral obligation. You may be able to shame her into complying, but you will have difficulty forcing compliance. What the broken promise does do is to make it easier for you to negotiate a firm date for the move.