It's no secret that regional elections in Germany are about not just local politicians and policies, but the national government as well. That's especially true of Sunday's vote in the central German state of Hesse and Angela Merkel's national coalition of conservatives and Social Democrats.

Both sides have been dramatically losing support, and hardly a week goes by without pundits pointing out that their so-called grand coalition no longer commands a popular majority. Indeed, a consensus is emerging that the era of big-tent parties capable of attracting 40 percent of the vote and more is swiftly coming to an end.

Hesse is, in essence, an opportunity for Merkel to show that her conservative CDU party and her governing coalition aren't as sickly as many of the pundits' diagnoses suggest. But for that to happen, she needs a number of factors to work in her party's favor.

A comeback for the CDU

Hesse is home to Germany's financial capital, Frankfurt, and a state where the CDU has taken at least 36.8 percent of the vote every year since 1970 and has governed since 1999. Conservative State Premier Volker Bouffier also remains relatively popular among Hesse's 4.4 million eligible voters.

But there is little chance on Sunday of the CDU matching previous results. Recent opinion polls project that six parties will qualify for Hesse's regional parliament, with the conservatives taking as little as 26 percent of the vote.

The silver lining of the dire poll numbers is that anything over that figure will be interpreted as a slight, not-as-bad-as-expected comeback. By bolstering turnout, Bavarian conservatives were able to buffer heavy losses and avert an absolute blow-out in regional elections there two weeks ago. Bouffier, who spent the week warning against "left-wing experiments," will be hoping for the same effect on Sunday.

In any case, Merkel needs the CDU to take the largest share of the vote, entitling it to claim a mandate to form the next government. Otherwise, popular dissatisfaction with her and her policies will be blamed for dragging down Bouffier, and pressure for her to step down as chair of the CDU will increase — all the more so because Bouffier is one of Merkel's closest allies and helped negotiate the national coalition.

The Social Democrats are hoping to halt the downward spiral

A non-disaster for the SPD

Even if the CDU outperforms in pre-election polls, the Hesse result could still imperil the governing coalition. Junior partners the SPD are reeling after taking less than 10 percent of the vote in Bavaria. That result was a humiliating disaster for Germany's oldest political party, which in its heyday was accustomed to getting 40 percent or more of the vote. It also led some Social Democrats to again call for an end to the SPD's cooperation with Merkel.

Read more: The surprising success of Germany's Green party

Well-liked lead candidate Thorsten Schäfer-Gümbel has repeatedly emphasized that "Bavaria is Bavaria, and Hesse is Hesse." Opinion surveys suggest he has a point. The Social Democrats are currently polling between 20 and 25 percent, enough to silence inner-party discontent without challenging the conservatives' pre-eminence. Something in that range would probably suit Merkel just fine.

The Greens are positioning themselves as an alternative to the grand coalition

A good but not great result for the Greens

The biggest danger to the SPD are the left-leaning Greens, riding high after their best-ever showing in Bavaria and projected to get between 15 and 22 percent of the vote. Their lead candidate, Tarek Al-Wazir, tops popularity rankings and personifies the Greens' new mainstream appeal. "We are the only party that hasn't been driven crazy by right-wing populism," Al-Wazir told voters at the start of the week.

The environmentalists are almost certain to record their best-ever performance in Hesse on Sunday, something Merkel wouldn't mind terribly, since a strong performance would make it easier for Bouffier to extend his current coalition with the Greens. Indeed, much to the chagrin of the right wing of her own party, Merkel is reputed to consider conservative-Green partnerships as the future of the CDU on the national level.

At the same time, though, she'll hope that Green gains aren't enough to eclipse the CDU or open up the possibility of a three-way coalition with the SPD and the Left party, which will likely clear the 5 percent hurdle needed for parliamentary representation. The most recent polls suggest that a so-called green-red-red coalition of all the parties on the left could be a possibility, meaning that Bouffier could be out, even if the CDU takes the largest share of the vote. One of the most fascinating points of this election is what it will say about the Greens' future orientation.

Germany's financial capital Frankfurt is Hesse's most important city

Disappointment for the AfD, the FDP as a player

The one party Merkel definitely wants to see stumble on Sunday is the far-right populist Alternative for Germany (AfD). A disproportionate number of AfD voters are disgruntled former conservatives, and because the CDU has ruled out any cooperation with the populists, a large AfD haul of votes would restrict conservatives' ability to form a stable parliamentary majority. Any instability in Hesse hurts Merkel's efforts to show that the political system in Germany is still functioning smoothly.

Read more: Merkel gets tough love from her party's youth wing

The final factor in the Hesse equation is the conservatives' traditionally preferred coalition partners, the pro-business, center-right Free Democrats (FDP). They are currently projected to get between 6 and 9 percent of the vote.

Watch video 00:27 Merkel: 'I need to do more to regain people's trust'

Merkel, who tried to form a national coalition with the FDP and the Greens last year, would probably not begrudge the Free Democrats their share of the vote as long as they don't eat into CDU support too dramatically. A so-called Jamaica coalition of CDU, Greens and FDP is, according to opinion surveys, another possibility after the Hesse election.

Whichever way it is divided, the political landscape in Hesse reflects that of the nation as a whole. With an unprecedented six parties likely to be represented in parliament, forming a coalition will be more complicated than in the past. If that process is led by the CDU and goes smoothly, it will be a victory for Merkel.

If uncertainty reigns, or conservatives lose control of the Hesse government, it will further weaken her hold on power as chancellor and party chair.

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