This Recent Study On the Shutdown Shows The Public Will Blame Republicans [View all]
"... According to our poll, a small plurality of Americans would still blame Republicans for the shutdown even if Democrats are withholding votes for health care funds:
If Democrats vote against a funding bill after Republicans refuse to restore health care funding, more Americans still blame Republicans (35%) than Democrats (24%), with 32% blaming both. (These numbers are similar to the topline blame results.)
Others have proposed that Democrats withhold support for the funding bill on the grounds that Trump is an authoritarian. Blame for Democrats rises in this scenario:
If Democrats vote against a funding bill as a broader statement of opposition to Trumps agenda (such as on immigration enforcement, deployment to cities), the split is 36% blame Republicans / 30% Democrats / 24% both.
Generally, the conventional wisdom that government shutdowns hurt the party in power or have a durable effect on public opinion is overstated. But if youre going to shut down the government, it helps to tie the move to something you want to deliver for voters. Democrats start with a real, if tenuous, lead on the shutdown fight.

The other way to view this shutdown polling is that, if there is going to be a shutdown, Democrats should fight for health care funding since it doesnt increase the percentage of Americans who say theyd blame the party for it. Put another way: If youre going to get blamed by some people for shutting down the government anyway, you might as well use the opportunity to accomplish something."
https://www.gelliottmorris.com/p/new-poll-voters-to-blame-republicans-for-shutdown
Corporate bias will headline the Republicans messaging, but at least we do have some numbers that contradict it.