The shared concern has even prompted the opening of a back channel: Members of the Bush and Christie campaigns have communicated about their mutual desire to halt Mr. Rubio’s rise in the polls, according to Republican operatives familiar with the conversations.

While emails, texts and phone calls between operatives in rival campaigns are not uncommon in the tight-knit world of political strategists, the contact between senior aides in the two campaigns has drifted toward musings about what can be done to stop or at least slow Mr. Rubio, the operatives said.

In a sign of a budding alliance, the aides have, for example, exchanged news articles that raise potential areas of vulnerability for Mr. Rubio. There is no formal coordination, the operatives stressed, but rather a recognition of a shared agenda.

“We do have similar goals,” an adviser to Mr. Christie said.