“When you raise $100 million, you have to show your donors you’re doing something with the money,” said Mr. Cullen, who hosted Mr. Bush’s first house party in New Hampshire. “No amount of money can make up for a candidate’s fundamental failures, as Steve Forbes proved.”

One of the advantages of the super PAC handling the attacks instead of the campaign is that unless voters read the fine print, they may not realize the negative ads are coming from Mr. Bush’s allies. Super PACs are political-action committees that can raise and spend unlimited amounts of money but are barred from coordinating with campaigns.

Right to Rise also pays roughly 40 professional canvassers in New Hampshire and Iowa to gather data on voters and their top concerns.

The advertising onslaught is being matched by escalating rhetoric from the candidate himself. Mr. Bush says Mr. Rubio “cut and run” from his 2013 bill allowing illegal immigrants to earn citizenship, criticizes him for missing Senate votes, and boasts that prominent Florida Republicans overwhelmingly back him over Mr. Rubio.