neither is convinced that the other guy will pay politically

[Irelia20150604]

Source: Trump's Unique Concept Of The Presidency Again On Display As Government Shuts Down

LIASSON: The problem for both sides is that neither is convinced that the other guy will pay politically. For Democrats, they know, as you said, that something like 90 percent of Americans are sympathetic with their position on the DREAMers but not shutting down the government over the DREAMers. And when people are polled about who would you blame.
==
Hi everyone! How should I understand the sentence in the context?

 

[Uncle Jack]

Both sides (Democrats and Republicans) are trying to work out which side will be blamed for the government shutdown. If one side thinks the other will get all or most of the blame and as a result will lose votes ('will pay politically'), then that side has no incentive to try to resolve the issue. The phrase in bold says that neither side is convinced that this is the case.

 

[Irelia20150604]

Got it. Thanks.