MONTCLAIR, N.J. — The African-American heritage parade on Saturday here drew to a momentary standstill. Philip D. Murphy, a Democratic candidate for governor, was darting back and forth across the street, responding to endless calls for handshakes, hugs and selfies.

Just in front of him was Jim Johnson, another Democratic candidate, who had barely broken a sweat after jogging nearly the entire route, so he could stop for hugs and handshakes as the parade wound through his hometown.

“People don’t forget when you shake their hands,” Mr. Johnson said, as he stood wearing a Rosa Parks shirt, a singular “Nah” quote stretched across the front. He added, “It was the hugs that slowed us down, it wasn’t the handshakes.”

With New Jersey set to vote on Tuesday in the nation’s first statewide primary election since the 2016 election, the candidates vying to replace Gov. Chris Christie, a Republican, were bounding around the state all weekend, holding multiple events each day and making their closing arguments to voters. From festivals to parades to train platforms to strolls along the iconic Jersey Shore boardwalk, the candidates promised bold changes to a state plagued by high taxes, an exodus of jobs, mounting debt, a troubled transportation network and nearly a dozen credit downgrades under Mr. Christie.