If you are looking for a noun for the division (besides division), perhaps you are thinking of schism? Google defines it as
a split or division between strongly opposed sections or parties,
caused by differences in opinion or belief.
At one time it applied more specifically to divisions within a church, and that's still sometimes the first definition in dictionaries1, but I think Google's definition captures a fairly common popular usage. The implication of a very deep division based on an ideological difference of opinion would seem to suit your question.
Usefully, according to the OED this noun has already been verbed:
intr. To separate schismatically.
1604 H. Jacob Reasons 77 He that differeth from the Gospell
ioyneth not to the Church, but schismeth from it.
And there is also the much more common adjective, schismatic.
Thus you could say something like
The schism between Republicans and Democrats over taxation seems
unlikely to resolve anytime soon.
Congress has schismed over the issue of taxation.
The schismatic issue of taxation is polarizing voters.
- The OED Online actually first lists an older, biblical sense of "a (metaphorical) rent or cleft."