Many people say that it is the polarization that causes the deadlock in American politics.
I'd say it is the combination of a bicameral, consensus-oriented system with a polarized political system. In the Westminster system for example the polarization wouldn't be a problem. One of the parties would just implement their politics.
Exactly. We have had (exaggerated by the electoral system, but it's the practicalities that matter, so let's ignore that) polarised politics in Britain since 1935, but there are no comparable issues with deadlock.