State Sen. Tom Holland is unopposed for the Democratic nomination. They will square off to succeed Democratic Gov. Mark Parkinson, who was finishing out the remainder of Kathleen Sebelius' term. She left office last year to become President Barack Obama's Health and Human Services Secretary.
In Missouri, Carnahan, the daughter of a former governor and a former senator, easily defeated two challengers. Her Senate bid comes 10 years after the death of her father and one of her brothers in a plane crash.
Carnahan, the two-term secretary of state, will face Blunt, who has served in the House since 1996 and whose son is a former governor. He beat eight opponents for the GOP nomination, including tea party favorite state Sen. Chuck Purgason. Four-term Sen. Kit Bond is retiring.
Missouri also became the first state to test the popularity of Obama's health care overhaul law.
Voters strongly approved a new law that prohibits the government from requiring people to have health insurance or from penalizing them from paying for their own health care. That conflicts with a federal requirement that most people have health insurance or face penalties starting in 2014.
The legal effect is questionable, because federal laws generally supersede those in states. But its passage sent a clear political message to Obama and the Democrats.