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Mr. Voss said Mr. McConnell is smart to link Mrs. Grimes to national Democrats and Mr. Obama.

“We have a whole lot of people who are registered Democrats, but who show little loyalty toward the national Democratic Party,” Mr. Voss said. “So the challenge for Grimes is to get voters to forget about that she caucuses with Obama’s allies in Washington, D.C., and have her seen as a moderate Democrat.”

Mr. Voss said that Mrs. Grimes can’t be counted out, pointing out that she has the stature to raise enough money to mount a serious challenge, and could make inroads with the voters that supported then-Sen. Hillary Rodham Clinton in the 2008 presidential primary.

He also said that she could also benefit from having “no ideological profile” as long as she can define herself before Mr. McConnell casts her in a negative light.