That's just the nature of the game I suppose, though it's not really a phenomenon that's particularly exclusive. There's nearly always going to be a disconnect from that initial novelty to the point where one becomes mired in the unimaginative bog that is routine. Getting a little bored is perfectly reasonable, and I think everyone has been there at some point. It probably doesn't help that we're coming off of one of the busiest months we've had in awhile (a lot of new items in the stores, snowballs, Toy Day, Countdown, and also the Harvest Festival a week or so before December) and we don't really have any events in January aside from New Year's Day and another fishing tourney.
I'm currently in the "grind for badges" phase as I try to fill up my catalog. Is there a point to getting 100%? Nah, but it gives me something to work toward. Some people are really into renovating their towns or homes, and that's another way to keep busy. Even then, some days are just "grab fossils, check stores, build snowperson, talk to villagers, end," but I suppose it helps that I'm always multitasking when playing. It definitely helps to play with others too I suppose. Most of my best experiences with the game involved meeting new people on the Club Tortimer island or just hanging out with people here. Granted, that's not always feasible, but even if it's something like "hey, can I pop in and catalog x?" it makes for a nice change.
Of course, I wouldn't worry about it if you can't set any goals that seem worthwhile to you. Tons of people take a break from it altogether and come back and find themselves enjoying it much more. In the end though, I guess it's just meant to be one of those games you play for a small amount of time everyday anyway, so it's not really problematic to become a little dismayed by a lack of things to do when it's symptomatic of the nature of the game itself. That said, think about the things that you like most in the game and focus your efforts towards them.
Then again, the stuff I'm saying probably ain't exactly hot off the press, kid on the street corner selling papers for a nickel sort of thing and everyone's aware of it, but I've rambled too much to not submit the post at this point.