During first week of the New Year, most people are enthusiastic about their resolutions. After this week, however, their zeal begins to dwindle, and soon they've forgotten all about their resolution. Thus instead of a New Year's resolution, it's a New Week's resolution, seeing as it only lasts a week.
Did you see the line of traffic for the gym?
It's just their New Week's resolutions.
I can't believe how many people in our neighborhood are recycling!
It'll end soon. It's New Week.