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With one income tax plan after another falling to Pawlenty vetoes, Mr. Dayton argues that middle-class taxpayers are disproportionately picking up the slack through higher state fees for a range of services and rising property taxes to offset deep cuts to local government allowances.

“It’s not a question of taxes or no taxes, it’s which tax on whom,” Mr. Dayton said.

Miss Kelliher and Mr. Entenza say they also would raise taxes on top earners too, but won’t go as far as Mr. Dayton or start on incomes as low. At a recent televised debate, both criticized Mr. Dayton’s plan as politically untenable.

“I don’t think any Legislature - Democratic or Republican - is going to tax $4 billion or $5 billion,” Miss Kelliher said. “I’ve been in the arena.”