Germans are set to vote in three regional elections seen as a test of support for Chancellor Angela Merkel’s policy towards refugees.
The anti-immigration Alternative for Germany party (AfD) is expected to make gains amid unease over Mrs Merkel’s so-called “open door” policy.
More than a million migrants and refugees entered Germany in 2015.
Asked on Saturday how she was preparing for Sunday’s elections, Mrs Merkel said: “I’m crossing my fingers.”
Polls suggest that her Christian Democratic Union (CDU) will remain the biggest party in Saxony-Anhalt in the east of the country.
It faces defeat to the Greens in Baden-Wuerttemberg in the west, where it is currently the largest party.
And in Rhineland-Palatinate, where the CDU came a close second last time, the race is on a knife edge.
Polls put the AfD’s support as high as 19% in Saxony-Anhalt, where the CDU and the Social Democrats now govern in coalition.
If the AfD performs as well as the polls indicate, the coalition partners may need to team up with a third party to assemble a majority.
Already represented in five of Germany’s 16 regional parliaments, the AfD has campaigned on slogans such as “Secure the borders” and “Stop the asylum chaos”.
German Vice-Chancellor Sigmar Gabriel said on Saturday that gains for the AfD would not change his government’s stance on immigration.
He said: “There is a clear position that we stand by: humanity and solidarity. We will not change our position now.
But in Berlin, about 2,000 right-wing demonstrators carrying German flags chanted “Merkel must go!” and “We are the people!”.
A failure to win at least two of the three states would be a blow for Mrs Merkel, just as she is trying to push through an EU deal with Turkey to reduce the numbers of migrants and refugees entering western Europe.
The chancellor alarmed many European leaders at a summit earlier this week by promoting a last-minute draft deal with Turkey to stop the migrant flow, and demanding their support.
Ms Merkel still needs to complete that deal at another summit at the end of this week. If her party performs poorly on Sunday, she will go into that meeting weakened.
The meetings and demonstrations came as thousands of migrants have massed in muddy camps in the Greek border town of Idomeni after countries across the Balkans closed their borders.