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Chancellor Angela Merkel is riding high in polls as she seeks a third term at the head of Europe's biggest economy. But a major state election this weekend may lift her center-left rivals' hopes of defying the odds and ousting Germany's leader.

Surveys show Merkel's conservative Christian Democrats leading in the polls in Lower Saxony, where voters choose a new state legislature Sunday. But the chancellor's party is unlikely to win an outright majority needed to form a new state government without the help of its coalition partners, the pro-market Free Democrats.

And that could spell trouble for Merkel.

The Free Democrats, who are also a part of the national coalition, have been losing so much support they may not win the necessary 5 percent to gain seats in the Lower Saxony legislature, an outcome that could drag the ruling coalition to defeat.

The situation mirrors a vulnerability Merkel herself may face in September when voters nationwide choose a new Parliament, which in turn selects the chancellor.

With six major parties competing for votes, German governments are invariably formed by coalitions. And Merkel's personal popularity may not be enough to overcome the weakness of the Free Democrats.

That's why so much attention has been directed at the vote in Lower Saxony, a northwestern region of 8 million people. The Sunday balloting is one of only two significant electoral tests before national parliamentary elections.

Recent polls in Lower Saxony show the Social Democrats and Greens neck-and-neck with Merkel's party and the Free Democrats. But the most recent surveys show the Free Democrats right on the 5 percent threshold.

A coalition loss in Lower Saxony would be a blow to Merkel and invigorate the center-left opposition of Social Democrats and Greens, who have been struggling to gain traction nationally.

The opposition leader in Lower Saxony, Stephan Weil, says a win would "fire up" his party and would mean that a center-left German government "will be taken seriously as an option after the national election."

Both nationally and in Lower Saxony, Merkel and her Christian Democrats have been bolstered by a relatively robust economy, low unemployment and the chancellor's hard-nosed handling of Europe's debt crisis — roundly criticized in debt-burdened European countries but which plays well among German taxpayers.

Merkel has made clear that her economic management will be a key plank of her national campaign.

She has also profited from the stumbling performance of the Social Democrats' candidate for chancellor, Peer Steinbrueck, the former finance minister whose personal popularity lags far behind Merkel's.

Over recent weeks, Steinbrueck has drawn criticism for saying the chancellor earns too little — adding to controversy over his own high earnings from the public-speaking circuit.

That has not helped a campaign that promises to narrow the gap between Germany's haves and have-nots. The Social Democrats and their allies, the Greens, want to introduce a mandatory national minimum wage, crack down further on tax evasion and raise some taxes — a move that Merkel says would be bad for the economy.

Her weakness, however, lies in the Free Democrats.

The smaller party is in disarray after failing to win major tax cuts it demanded at Germany's 2009 election and taking much of the blame for persistent coalition infighting.

Gero Neugebauer, a political scientist at Berlin's Free University, said the party "has a problem, which is it doesn't have a profile that is sufficiently attractive for enough voters."

"The government's work as a whole, particularly that of the chancellor, is viewed very positively by the majority of the population," the general secretary of Merkel's Christian Democrats, Hermann Groehe, said recently.

But, he added, "the Free Democrats must ensure that they also benefit from this successful record."

If the Free Democrats stumble, party leader and vice chancellor Philipp Roesler, whose home state is Lower Saxony, is widely expected to lose his job. The party's poll ratings haven't improved since he took over in 2011.

Merkel's preference is to continue her alliance with the Free Democrats, her party's traditional partner. If the Free Democrats run poorly in September, she could try to revive her 2005-9 "grand coalition" with Steinbrueck's Social Democrats, a combination popular with voters but not with either party's rank-and-file.

The Social Democrats are more open than Merkel's coalition to pooling European countries' debt as the continent claws its way out of its financial crisis.

Nevertheless, analysts are skeptical as to how far Germany's European policy would shift with a change of power.

Economists at Deutsche Bank said in a recent research note that Merkel and Steinbrueck differ more on style than substance, and that the country's supreme court and public opinion "will continue to constrain policy."