Mmmm yes.
We can look at it the same way we look at bad movies and games. There are certain elements that make a song good; melody, rhythm, dynamics, harmony, emotion, and technique(there are a few more but these will do). some of these elements are there by default, like melody and rhythm, but dynamics and emotion have to be created. Even with the elements like melody and rhythm you can stuff up, there are some notes that just don't work together and you can easily make a rhythm sound bad. Sometimes if you muck those you up can recover by having great emotion and/or technique, but if there is none of that, then you are in trouble.
So if we start to remove the elements, we can start to get some really bad songs.
The song has notes that clash and the melody is not catchy at all, the rhythms are blocky and rough, there is no dynamics, as in it is the same level the whole song, the harmonies are rough (to many 4ths!), there is no emotion and the playing is sloppy and dull.
Of course, just like the worse movie or game, you will have people who like this song, no matter how shitty it is. On the same page, you can have a song with all these elements and still have people hating it, for example, most pop songs have these (however emotion and technical ability are disputable), but people still hate it. Dispite what you may thing, most pop songs are 'perfect' in the fact that their production is flawless, and the musical side all fits, yet people still don't like them.
In conclusion - You can have a bad song, even though there will be some people who still like it.