It took Tammy Murphy just weeks to win the backing of key New Jersey Democratic leaders in her bid for Senate. In a state where party bosses still carry strong influence in elections, that could ordinarily be enough to ensure her nomination — giving the New Jersey first lady preferential ballot positioning right below President Joe Biden in many critical counties.

But Murphy is leaving nothing to chance in her battle against Rep. Andy Kim and is now looking to possibly take even greater advantage of New Jersey’s unusual primary ballot system to give her an edge.

To do so, Murphy is considering appearing with Biden on the primary ballot across the state even in counties where she doesn’t gain party endorsements, according to three people familiar with the private discussions among Democrats. It is a seemingly small visual distinction but one that could lead many voters to ignore Kim, who would be forced into a separate column without the president.

Such a move would require the consent of the Biden campaign, giving the president tacit but significant influence over the high-profile primary to replace indicted Sen. Bob Menendez. The outcome will test the influence of Murphy, a former financier who’s long been a player in Democratic circles. Her husband, Gov. Phil Murphy, served as the finance chair for the Democratic National Committee and was a member of the Obama administration.

The Biden campaign told POLITICO it is working to get on the primary ballot in the state but does not plan to weigh in on the Senate primary.

“The campaign is........

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