Germany's Nazi past made it impossible for any half-way respectable far-right party to gain traction before the AfD. It scores 7 percent in opinion polls but pollsters say it could potentially reach 22 percent.
Merkel first ignored and then ostracised the AfD, which draws support from all parties and non-voters. But improving election results have undermined her strategy.
"If they want to remain successful, they need to find a way to unite and keep both wings of the party," a Merkel adviser told Reuters.
Germany's politics are shifting. The Free Democrats, long the CDU's coalition partner, are in disarray after election defeat in 2013. Many FDP voters switched to the AfD, with which the CDU has ruled out a coalition.
On a cold night in Germany's second city, it took a while for the Hamburg crowd to warm to Lucke's warnings of Greece's fiscal mess, euro zone deflation, Germany's low birth rate and the low skill levels of immigrants.
Lucke finally roused the crowd by saying Greece should be thrown out of the euro -- a popular view in Germany -- but predicted Merkel will try to prevent that because it would show the failure of her rescue efforts.
Lucke's lack of charisma may be an asset in a country wary of such things after Hitler.
"Lucke is the antithesis of a charismatic politician," wrote the conservative Frankfurter Allgemeine Sonntagszeitung. "You wouldn't want to go have a beer with him because he's the kind of guy who would order a fanta instead."
One reason why analysts believe the AfD won't quickly self-destruct is that there are experienced CDU veterans in its ranks. Like Alexander Gauland, AfD leader in Brandenburg.
"We believe there should be two wings to this party reflected in the leadership," Gauland told Reuters.
Gauland, born in Communist East Germany but who fled to West Germany and spent 40 years in the CDU, said the AfD thrives in the east because it attracts "conservative, patriotic and -- I mean this cautiously -- nationalist voters."