“They don’t need to get 5 percent to make things very tight for the chancellor,” said Wolfgang Nowak, a fellow at the North Rhine-Westphalia School of Governance in Duisburg. “And every swastika on the street in Athens helps this new party.”

One new member, Martina Tigges-Friedrichs, said she belonged to the Free Democratic Party in the state of Lower Saxony for 15 years before she quit this year, frustrated that the pro-business party had abandoned its principles. She said she was attracted to Alternative for Germany because of the prominence of its founders, and because the current center-right government had put the country on a dangerous financial course.

“We keep giving out more and more money when we have so many problems here at home,” said Ms. Tigges-Friedrichs, who runs two hotels and a cafe in Bad Pyrmont.

The new party illustrates the increasing fragmentation of the political scene in Germany, Europe’s economic powerhouse. But the rapid ascent and equally rapid descent of another protest group, the Pirate Party, whose vague platform is focused on greater openness in government, offers a cautionary tale for the professors and professionals behind Alternative for Germany.

Polls show that a large number of voters, as many as one in four, would consider voting for the party. But that might not translate into actual votes. And several other surveys have shown that the nostalgia for the former German currency, the mark, is beginning to ebb.

Discontent has its limits. While Germans dislike the notional price tag for the many commitments and guarantees their government has made over the three years of the euro crisis, the job market is strong, borrowing costs are low and the country is approaching the balanced budget it so desperately craves.

Alternative for Germany has also called for simplifying the tax code, restructuring energy subsidies and favoring the most qualified workers for immigration, but ultimately it is known here as an anti-euro party despite efforts to paint itself as a broader movement.