Margaret Thatcher was finally undone in the UK by her insistence on attempting to finance local government expenditure with a poll tax. This proposal led to civil disobedience and mayhem because a poll tax is a deeply regressive tax: Everyone pays the same amount regardless of income.
In the US, the termPoll tax is according to Wikipedia more associated with taxes on voting but I'd like to suggest its actually very applicable to the mandates + fine with no PO construction thats apparently in the senate HCR bill.
The subsidies for those on lower incomes are not really large enough as they stand. But in the absence of meaningful restrictions on the insurance companies to raise rates, the profit maximizing act for insurance companies will be to raise the premiums on those policies/make them crappier in order to extract most of the subsidies themselves.
So, put simply, the choice people will have in this situation is:
Buy Junk Insurance or Pay the Poll Tax.