BERLIN - Germans voted a new parliament in the state of Schleswig-Holstein on Sunday, with Angela Merkel's conservatives fighting to prevent a loss of local power to their Social Democrat rivals that could dent the chancellor's 2013 re-election hopes. Merkel's resolute stance through the dramas of the euro zone crisis has left her personal popularity intact. But her national centre-right coalition is in jeopardy after a slump in public support for her junior coalition partners, the Free Democrats (FDP), due to their infighting and prickly leaders. To have any chance of a third term in power and press on with her drive to instill German-style budget discipline across the ailing euro zone, Merkel must find new allies for her Christian Democrats (CDU) and end a dismal run at regional level for both her party and the FDP. Schleswig-Holstein's voters looked almost certain to eject the CDU-FDP alliance that has run Schleswig-Holstein since 2009. First exit polls are due at 1600 GMT. The question is whether the CDU can remain the largest party in the largely rural state of 2.8 million people on the Danish border and cling to power in a different coalition. "I believe we will win, that we will fulfill our goal and be the largest party by a strong margin," said Jost de Jager, the CDU's lead candidate in Schleswig-Holstein. If the party does win it would most likely strive for a "grand coalition" with the Social Democrats (SPD). But if the SPD become the largest party they will try to form a "Danish traffic light" coalition with the Greens and the South Schleswig Party (SSW), representing the Danish minority. A CDU victory would give the party a vital second wind, at a sensitive time for the chancellor. With national elections in France and Greece and local elections in Italy on the same day, the Chancellor faces a backlash across the continent to the austerity measures she has championed as the bitter pill necessary to solving the debt crisis. Merkel could lose her ally Nicolas Sarkozy in France's presidential vote on Sunday with leftist leader Francois Hollande tipped to win, who has pledged to try and temper the austerity drive. Merkel also faces a vote in Germany's most populous state North Rhine-Westphalia, frequently a barometer of future national voting trends, where the CDU trails the SPD by 7-8 percentage points.