In a clear sign that frugal government and fiscal responsibility can appeal to voters — in Germany at least — Chancellor Angela Merkel has won a resounding personal victory, equaling Britain’s Margaret Thatcher, by being chosen on Sunday for the third time to lead her nation.

But Ms. Merkel’s historic electoral victory — with her two parties, the Christian Democratic Union and the Christian Socialist Union winning their highest number of seats in many years — was clouded by the failure of her key coalition partner, the Free Democrats, to retain their seats in the Bundestag.

That left her five seats short of a government majority. And the choices on the left are not good news for her continued efforts at austerity and keeping the Euro bloc together.

That outcome might not turn out to be good news, either, for British Prime Minister David Cameron’s effort to persuade voters to ratify that nation’s continued membership in the European Union in a forthcoming referendum.

The first choice in Germany would be a “grand coalition” with the weakened second-place party, the Social Democrats, who suffered a major electoral setback on Sunday. But the SD may prove to be reluctant and demand difficult changes, including more government spending.

A less likely possibility would be a coalition with the Green Party, whose policies are generally anti-Merkel. The most unlikely option would be a coalition with the old Communist Party, now known as the Left Party.

But according to German news outlets, as of Wednesday the road to forming a coalition still looked like a long one.

Ms. Merkel has said she wants to talk with the Social Democrats. If their demands are unacceptable, she may call for another election and hope that German voters will push her bloc over the top for the first time in a half-century.

Until the composition of the next German government is settled, this election’s effects on Europe remain unknown.

But great questions face Germany and the European Union, with its dangerous divisions between frugal, productive nations and a southern bloc that has carelessly run up debt without improving output.

One thing is clear: Most Germans admire and respect Ms. Merkel — and her message of fiscal responsibility.