LOST PINES, Tex. — After two bleak years, Republican governors gathered here on Thursday to assess their political future — and they liked what they saw. With 37 governors’ seats open in 2010, the party is looking to topple some big-name Democrats.

Gov. Haley Barbour of Mississippi warned against attacking President Obama.

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What was most striking about the Republican governors was not simply their sense of optimism — a sentiment that would draw no Democratic quarrel these days — but exactly how they saw their road back to power and unity. The talk here was of the health care plan...