At Donald Trump's first political rally since COVID-19 shut the country, they decided to play Tom Petty's "I won't back down". Unfortunately, the rally organizers didn't have the right to do so, and not surprisingly, they received a cease and desist letter from Tom Petty's family (see link).
While the campaign may have thought it could use the venue's public performance license, such licenses generally exclude music use during conventions, expositions and campaign events (see ASCAP document). To avoid this issue, campaigns can obtain a political campaign license. However, musicians can request specific songs be excluded from a particular campaign's license. And, even if a campaign is properly licensed, the artist can still raise legal claims against a political campaign for using the musician's music. In other words, the only way for a political campaign to be safe is to request permission from the artists.