Keep going no matter what day it is
In January in particular it's important to keep in mind that it doesn't really matter what day it is. You might have a surge of energy on the first day of the year, or the first day of a new month, or on Mondays, and decide "I'm starting the new habit today!" Great -- go for it!
But ... what happens when Thursday hits and you're exhausted and you have a fight with your sister on the phone and suddenly your determination to skip the wine, or to make a healthy dinner, or to take a walk is gone?
The all too common scenario is she drinks on that day, and then says "Oh well I'll try again next Monday." (or next month.) And continues drinking for the rest of the weekend.
It doesn't matter what day it is. Do the right thing today, no matter what happened yesterday.
When you've fallen, get back up and try again. Absolutely don't talk yourself into another few days of drinking because it isn't Monday yet. Start now. If you wait 'til Monday you'll just spend more time in hungover/anxious/sick/sad mode and less time feeling good about keeping your promise to yourself.
Maybe your new year's resolutions are already out the window -- and most people's are by this point of the year. You can't go back in time and change that now. Remember the aphorism "don't look back; you aren't heading that way." Look ahead, remember why you're making the change, and make it. Today. I believe in you!