It’s pretty clear, from a recent Brown University poll that about one-fifth of the electorate in Rhode Island are in the die-hard public sector camp:

On the other hand, a large percentage — 73.3 percent — opposed raising the state sales tax, while 18.9 percent supported the idea. And 74.7 percent opposed raising the state income tax, while 19.3 percent supported the idea.
When asked about measures that would affect state employees, 46.6 percent supported unpaid furlough days, while 38.4 percent opposed the idea, and 57.9 percent supported a defined-contribution pension plan for new state employees, while 21.1 percent opposed the idea.

Basically, 20% of survey respondents want higher taxes to support the deals currently offered to public-sector employees. I can’t say, of course, how much overlap there is between wanting to increase the sales tax and wanting to increase the income tax, but I’d wager that it’s significant — constituting, overall, a statement of “whatever it takes.” That’s a significant portion — especially given its greater likelihood actually to vote and to become active before election day — but it’s not overwhelming.
The route to countering that bloc will be to isolate their issues in the face of a single candidate — who, incidentally, has made it abundantly clear that he’s their guy:

… during and after the Marriott Hotel lunch, [Lincoln] Chafee insisted that [Frank] Caprio’s $100 million in promised [pension] savings are illusory, because his plan “won’t standup to legal scrutiny.”
“It’s hard to believe that a court would agree that somebody that has been paying into a certain pension fund for 30 years, all of a sudden has a new pension plan. It’s hard to believe a court, beyond the fairness issue, would say that is legal,” Chafee said.

Determining, beforehand, that the union’s ever-present threat of expensive litigation will prove indomitable is a classic ploy of union-bought candidates for office. It simply is not difficult to believe that an objective judge would allow the state to change the terms of an insupportable pension system, at least for investments not yet made. In other words, the fact that employees have been paying into a system does not mean that they have a legal right to see that system perpetuated. Some aren’t yet vested, which means that they don’t even have a claim to the fruits of their investments thus far, and others can be told that different rules will apply to payments made from this moment forward.
The more extreme measure — which may yet prove necessary — would be to transfer the vested payments into a defined-contribution plan that is financially comparable, but with better terms for the state. But I don’t think any candidates have gone that far.