The Stern and RTL poll shows Rösler's leadership has so far barely made a dent in Germany's tepid feelings toward the party.
The party achieved great success in the 2009 federal elections, achieving 14.8 percent of the vote under Guido Westerwelle. But Westerwelle was forced from his leadership position in May after Germans' support waned.
He has become one of the most unpopular politicians in Germany, with only 28 percent of voters saying he's doing his job well, according to the poll.
In contrast, Chancellor Angela Merkel's Christian Democratic Union (CDU) improved one point over last week to 33 percent while the Social Democratic Party (SPD) also gained a point to 25 percent.
In one bright piece of news for the party, Rösler, who is also Economy Minister, has won praise for his plan to shore up faltering Greece by promoting more investment. The respected Cologne Institute for Economic Research lauded the plan as a ''win-win'' for Germany and Greece.