BERLIN, Germany — What Americans know about Angela Merkel: Named by Forbes as the world’s most powerful woman for the fourth straight year, she was the world leader who grimaced at then-U.S. President George W. Bush’s shoulder rub.

What Germans know about "Angie": She is a confident chancellor who has made steady assurances that she would guide the world’s third-largest economy through the financial crisis.

But they don’t know much more about her than that.

While Germans have embraced Merkel’s displays of quiet authority, they haven’t been able to overcome the aura of personal and political aloofness that she projects. Germany knows that its chancellor is powerful, but the recent election campaign did not show them her vision for German society and her ideas for solving the country’s most fundamental structural and social problems. And that lack of clarity over what she stands for could get Merkel in trouble during her second term.

The general contours of her biography are clear enough. Raised in East Germany as the daughter of a Protestant pastor, she pursued a scientific career as a physicist in East Berlin.

After the fall of the Berlin Wall and the reunification of the country, Merkel quickly rose through the ranks of the country’s governing conservative party, the Christian Democratic Union, serving as environment minister from 1994 through 1998. The way Merkel coolly dispatched rivals both within and outside her party on her way to the top earned her respect among her colleagues — as well as a reputation for harboring a political identity motivated more by the maintenance of personal power than by any specific conservative principles. Her strategy may be explained as necessity: The earthy, western German, male Catholics who long dominated the party were not inclined to be long forgiving to the intellectual, eastern German, secular Protestant woman who had managed to take the reins.

Merkel already had one strike against her for the poorly managed campaign she ran four years ago that fumbled away the conservatives’ strong lead in national polls and forced the CDU into an unwieldy coalition with its rival, the center-left Social Democrats (SPD).

Last Sunday’s election will only exacerbate traditional CDU members’ suspicions that Merkel has had an agenda to change party. Since climbing the merciless path to the top of the CDU hierarchy, Merkel has tried to attract independents by softening her party’s stance on social issues.

Where the CDU’s leadership used to routinely claim that Germany was not “a country of immigration,” Merkel organized conferences with the Muslim community in Germany to discuss social integration. Where the CDU was once skeptical that Germany could afford measures to counteract global warming, Merkel has presented herself as the “climate change chancellor.” And where the party used to go out of its way to show its reverence for the institutions of the Catholic Church, Merkel did not hesitate to criticize the current German-born Pope Benedict XVI for reinstating bishops who had denied the Holocaust.

But, in her term as chancellor, Merkel has not been nearly as vocal on issues traditionally closer to her conservative party’s heart, such as reforming the country’s labor markets and simplifying its tax code. Merkel has claimed she had no choice. She ran in 2005 on a platform of free-market reforms, she insisted, but the voters had forced her to work with the SPD.

Nonetheless, on Sunday night when the election tallies came in, it was the doubters of Merkel’s commitment to the conservative creed who felt confirmed. Merkel’s support among her own Christian Democratic base, which was not strong to begin with, eroded even further this year. Merkel’s CDU only earned 33 percent of the vote, the second worst showing of the party’s history. Merkel, it seems, has failed to pass the authenticity test among loyal conservatives.

And, indeed, when Merkel took the stage at the party headquarters less than an hour after polls closed across Germany, her primary concern seemed to be assuaging the country’s moderate independents. She was there ostensibly to announce and take credit for having achieved her election goal — namely, a coalition with the free-market Free Democratic Party — but Merkel’s demeanor momentarily belied the festive occasion. She bore a diffident expression and her message was less than celebratory. Unprompted, she anxiously emphasized that she intended to serve as “chancellor for all Germans.”

It was a phrase that neatly summed up the unsustainable character of Merkel’s tenure at the top of Germany’s government. For four years, she has been chancellor for all Germans, but no one party. Merkel’s demure, consensus-seeking style at the top of the “Grand Coalition” between SPD and CDU earned her personal approval ratings that were consistently near 70 percent. But, at the same time, the polls from Sunday show that she has failed to strongly convince any single group of Germans that she was their chancellor in particular. It seemed Germans liked her precisely because they weren’t sure what she stood for.

Merkel may continue to try to rhetorically stake claim to the lofty above-the-fray role she has carved out for herself, but she will likely find herself having to offer more partisan red meat to keep her grumbling conservative base, as well as her free-market FDP coalition partners, at bay. Indeed, Germans will likely have to adjust to a chancellor less like the conciliatory moderator between the center-left and center-right whom they came to know recently, and more like the polarizing Margaret Thatcher-style “Iron Chancellor” figure that she was first depicted as four years ago.

The economic faction of conservatives will soon demand their pound of flesh in the way of structural reforms of the economy. With the SPD’s weak showing in the election, they’ll argue that there are no more excuses for delay. But, Merkel, true to her cautious temperament, has already indicated that Germany likely won’t be able to afford any more tax breaks given the country’s large budget deficit in the wake of the financial crisis.

How long Germany’s conservatives will pay deference to Merkel’s personal popularity in the country at large is an open question. But, if they do attempt to pressure the chancellor, they ought to be prepared for pushback. Merkel’s vision for the direction of German society may lack inspiration, and her rallying cries may fail to stir her voters, but her critics and allies alike have always given her credit as a canny strategist of intra-party politics and a merciless defender of her own personal authority. Famously, she secured the party leadership for herself 10 years ago by decisively staging a putsch against her mentor and patron, former chancellor Helmut Kohl, when he was embroiled in a financial scandal.

It’s not for nothing that Merkel has found her way to the top and stayed there. As the “chancellor for all Germans” she may not articulate a clear political philosophy, but she certainly does have sharp elbows.