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“She knows how to get this job done,” said her spokesman Brian Doory. “This district has been underserved for some time. … She’s a business-minded, fairly conservative Democrat who is endorsed by the National Rifle Association.”

Just as Mrs. Halvorson has touted her political clout as the state’s Senate majority leader, Mr. Ozinga has pushed back, labeling her as a career politician with ties to a failed government.

“Republicans still like their chances because they feel she has an incredible amount of baggage,” said Mr. Gonzales, who calls this race a tossup but tilting slightly Democrat.

In Minnesota’s 3rd District, it has been an expensive battle between Republican Paulsen and his Democratic challenger Madia with polls showing a dead heat. Republicans have held this seat for 50 years.

The contest has grown contentious in recent months with a spate of negative ads.

Paulsen spokeswoman Stacey Johnson describes it as “Minnesota mean.” The Democrats are better funded, but she said Mr. Paulsen has received a lot of support within his party.

Madia spokesman Dan Pollock said that as a former Marine and war veteran, his candidate can take political attacks and is buoyed, as a political newcomer, by the grass-roots support.

“The Paulsen campaign ads are tough stuff, but he’s a Marine Corps officer so he’s used to taking some punches, and I think he’s handled it just fine,” Mr. Pollock said.