BERLIN — To get Berliners arguing, bring up the new $3.4 billion airport rising just beyond the limits of this hip but economically strapped metropolis.

Supporters of Berlin-Brandenburg International Airport contend that it might be the salvation of a city that, despite its incredible historical resonance, has become an economic and geographic backwater. Detractors vehemently argue that the airport will be just another misguided drain of money by a local government critics say has failed to help Berlin realize its potential despite the city’s status as one of the hottest destinations on the planet.

City planners designed the airport as a symbol of their dream for Berlin, restored to greatness as the capital of a unified Germany. And so the fight now is about how Berlin has actually turned out: Germany’s cultural magnet and international beacon but also its national poorhouse, struggling to break out of a long slump. Berlin has the highest rate of residents on welfare — 18.6 percent — and received some $4 billion in state subsidies last year.

In a time of rising budget deficits, Germans are loath to bail out Greece in part because they have been bailing out their capital — and other stagnant parts of the former East Germany — for two decades.