Are you trying to get specific villagers to move or just villagers in general?
If it's villagers in general, you can use any variation of that method. Villagers will ping you when they're thinking about moving. Sometimes, someone starts thinking about moving the day after you deny someone's request to move, sometimes it takes longer. I had villagers refuse to think about moving for more than just three days, for example.
Has anyone pinged you recently? If not, I wouldn't recommend that method. Someone might be thinking about moving without your knowledge and in that case, even a few days can make a difference between accidentally moving them out or not.
If I were you, I'd change the 3DS date to two or more weeks from now and start the game as a new character. When Porter hands you the map at the station, check it to see who's missing. Quit without saving and set the clock back to your previous date. You can load the game as your mayor and find that villager, and they'll ping you. If they don't, talk to them a few times, save, reload, and find them again. Keep doing that last step until they do ping you. That method is safer because at least you'll know which villager was planning on moving out, and it's also easier since you don't have to walk around talking to lots of villagers. If nobody is missing from the future map, that's because nobody is thinking about moving on your current date (you can walk around and see if anyone's at home and in boxes, just don't go to the town hall). In that case, you can try again tomorrow or TT to tomorrow as your mayor, save, and use a new character to check your town's future version.
How many villagers do you have? Are there any events coming up in your town?
