Yep, it's going to depend on the situation and the hiree in question, as has been mentioned. If it's an R1 and/or if research will be a big part of your job, then they're likely going to want to see a decent scholastic record and well-defined area of interest. Conversely, if it's perhaps a small liberal arts college where teaching is going to be emphasized, then prior teaching experience will likely trump having a staggering list of pubs.
You also have to factor in the area of the country and your particular niche (you could luck out and be one of a very few number of folks in your research area looking in that geographic region, for example). But by and large, faculty positions are pretty competitive. As Pragma mentioned, a postdoc is likely going to make you more competitive, but as erg pointed out, it's certainly not necessary in all cases.