Considering the composition of the Legislature, how strong is the Governor of RI really?
Rhode Island is a one party state. Many people who would run as Republicans in other states run as Democrats here. Due to that, our last governor was able to get many conservative tax policies passed. It's kind of a good situation for Republicans. They can get their agenda passed and when it fails they can blame it on the Democrats.
Hell, just last year the legislature passed a voter ID law, and that's unheard of in other states controlled by Democrats. In addition, all of the opposition to marriage equality earlier this year came from Democrats.