Scott Brown, fresh from his improbable election to the US Senate, knew where his first stop should be: breakfast with Boston’s powerful mayor, Thomas M. Menino.

They seemed an odd couple that morning in January 2010. One was a suburban Republican with fashion model looks, a rising star on the national stage. The other was a big-city Democrat with a style all his own. But facing cameras after eggs and turkey sausage, Menino described Brown as an “old friend.’’

Since then, Brown has regularly called Menino. To run his state office, Brown hired a former Boston city councilor, who knows from experience what it takes to stay on the mayor’s good side. And Brown has made a habit of joining Menino at community events: Last Thanksgiving, they carved turkeys side by side at the Pine Street Inn.

The mayor had gone so far as to declare the Republican senator unbeatable. But that was before Elizabeth Warren, a favorite of the national Democratic Party, entered the race, pulling even with Brown in polls.

Now Menino, whose endorsement is capable of delivering thousands of votes on Election Day, faces a choice: Does he go all out for Warren or hold back, in deference to Brown?

Menino’s personality may mesh with Brown, but his politics align with Warren, a hard-charging consumer advocate. Some of Brown’s votes in the Senate have been at odds with issues dear to the mayor, such as supporting budgets that slashed money for public housing, community health centers, and grants for urban social services.

But Menino has a history of playing hard to get with Democrats running for statewide office. And he has proved in the past that personality can trump party.