The Rama (y.d. 98) writes that foods with a very strong flavor such as spices are not batul in 60x because the flavor is still able to be tasted, however the Rama limits this to when the item is prohibited in and of itself (i.e. teruma or avoda zara), to the exclusion of spices that just have a non-kosher item absorbed in it. The source for the Rama is our gemara where we see that "grissin" which fall into lentils can give flavor even if there is 100x as much to be mevatel. Clearly, the idea of 60x is an assumption but doesn't apply to cases where the flavor is actually tasted. But, regarding the Rama's stipulation that this rule would not apply to foods that have the taste of issur absorbed in them, but are not assur themselves, the Gr"a quotes those who disagree. The Gr"a writes that in our gemara we find that fish brine isn't going to be batul until there is 192x as much, even though the actual water and vinegar in the brine isn't technically assur, just that it has the flavor of the fish fat absorbed inside of it. The same should apply to a spice which has the flavor of non-kosher meat - so long as the spice could be tasted in whatever dish it falls into, it should be assur even if there is 60x as much.
The Shach writes that when spices are able to assur foods even when there is more than 60x, it is only an issur d'rabonon. R. Akiva Eiger quotes the Ran who disagrees and holds that it would be d'oraysa. The Ran is easy to understand, but the Shach is harder to understand - why would it only be d'rabonon? It seems that the Shach understands that once there is 60x of the mutar food to the assur food, the flavor is weakened to a point that it isn't considered true ta'am and therefore it is only assur m'drabonon.