In another challenge to her conservatives, a far-left party with roots in East German communism hopes to lead a government in one state, Thuringia, for the first time since the Berlin Wall came down 25 years ago.
For Merkel, the elections will be the latest of support in eastern states that, a quarter century since Germany's reunification, still lag the west in wealth, jobs and wages.
The eurosceptic Alternative für Deutschland (AfD), which less than two weeks ago entered a German regional parliament in Saxony for the first time, looks set to repeat the performance in Thuringia and Brandenburg, polls show.
The AfD have gained in the polls in recent weeks and now stand at around seven to eight percent in both states. But the party has ruled out forming a coalition with anyone post-election.
Since it was founded early last year, the AfD has campaigned for Germany to exit the euro, but stay in the EU, while promoting "family values" and flirting with populist positions on issues such as immigration and law and order.
In their campaign literature for Thuringia the party complains that "political corrrectness lies like mildew on our land".
It appears to have clawed away votes from the far-right and openly xenophobic National Democratic Party, which was kicked out of Saxony's parliament, having fallen just short of a five-percent hurdle to gain seats.
"The AfD is a problem for all parties," Merkel, who herself grew up in the former German Democratic Republic (GDR), told public broadcaster RBB this week.
She said the popularity of the AfD - which scored almost 10 percent in Saxony on August 31st and is polling at 7-8 percent now - is a reminder that "we must address the problems that concern the people".
"They worry about crime and rising numbers of asylum seekers," she said,referring in part to an influx of asylum seekers from eastern Europe and war-torn Syria.
"We must not only address these issues but also find solutions. Then we'll have a good chance of winning back those voters who are perhaps dissatisfied."
Sunday's polls will be closely watched as a measure of the strength of the AfD, which only narrowly missed out on entering national parliament last September and won seven European parliament seats in May.
"In the former GDR, volatility is higher than in the rest of Germany and voters are more likely to switch parties, making it an excellent testing ground," said Ulrich Sarcinelli of Koblenz University.
In Thuringia, voter discontent has raised the prospect of a state government led by the far-left Linke party, which groups former eastern Communists and anti-capitalists from western states.
While Merkel's conservatives remain the strongest force there, the Linke, polling above 20 percent, hopes to beat them by teaming up with the centre-left Social Democrats (SPD) and the Greens.
Under such a scenario, the Linke's Bodo Ramelow would head Germany's first so-called "red-red-green" government as the senior partner, making a similar three-way alliance thinkable at the national level.
"This would be a signal and could pave the way for a change at the federal level," Sarcinelli told AFP.
Merkel's party was forced last year to enter a "grand coalition" with the SPD because of the ballot-box demise of her former allies, the liberal Free Democrats.
So far the SPD has rejected a national level tie-up with the Linke, citing the far-left party's more radical policy ideas such as a basic salary for everybody and a ban on any German military missions abroad and Merkel urged the SPD not to switch allegiance.
"To put it mildly, I find it remarkable and a little strange when a large mainstream party like the SPD thinks about supporting a leftist state premier," she said. “As a mainstream party, who would do that to themselves?"
The SPD, meanwhile, is virtually assured another victory in Brandenburg. It is expected to easily hold onto power in the state that encircles Berlin and which has been a Social Democratic bastion for 24 years.