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“I’m not going to sit on the sidelines and let liberals control our state and our national government while I sit in my armchair being ideologically pure,” said Russell Johnson of Everett.

The challenge from the right has forced Mr. Rossi to shift. He has signed on to the tea party-inspired “Contract From America,” which includes pledges to enact a flat income-tax rate, repeal the new health care law and reject a cap-and-trade system for carbon dioxide emissions.

Polls have shown Mrs. Murray and Mr. Rossi with commanding leads over the rest of the primary field and essentially tied in a head-to-head matchup. Mrs. Murray has about $6.8 million in campaign cash as of June 30 while Mr. Rossi banked about $1.3 million in his first blitz of fundraising after entering the race in late May.