Germany finally has a leader. Now comes the hard part for Friedrich Merz

After some dramatics, and around 10 weeks after the German election, Europe's largest economy finally has a leader: Friedrich Merz.

His ascension didn't come easy though. On Tuesday, Merz failed to be elected chancellor in a shock first-round vote, an unprecedented event in the country's modern history. Despite securing the necessary parliamentary support in a second attempt later in the day, Merz appears to be starting his new role somewhat bruised.

"It's the weakest possible start," Carsten Brzeski, global head of macro at ING, told CNBC.

Other observers like Cyrus de la Rubia, chief economist at Hamburg Commercial Bank, appear less concerned.

"I think that in a week or so from now, nobody will talk much about it anymore. Instead people will look at what the government is deciding and doing," he told CNBC.

Either way, the hard work is really only just beginning for the new chancellor and head of the coalition government that is made up of his Christian Democratic Union, with its affiliate the Christian Social Union, and the Social Democratic Party.

Some of the challenges include addressing division within the country about issues like migration, geopolitical tensions around defense spending and trade, a stagnating economy and keeping the ruling coalition united and in line.

Germany's economy will be top of mind for Merz, having made promises of reforms and new investments, and having harshly criticized the previous government's policies during the election campaign.

For over two years now, the country has seen alternating economic expansion and contraction each quarter. Annual gross domestic product growth was negative in both 2023 and 2024. And latest forecasts don't seem to indicate much respite ahead.

This is despite the major fiscal package pushed through by the CDU/CSU and SPD during their coalition negotiations, which includes changes to long-standing debt rules to allow for more defense spending and a 500 billion euro ($567 billion) infrastructure and climate investment fund.

That cash at least appears to be safe, but questions have emerged about other fiscal and economic policies, ING's Brzeski said.

"I think that the 500bn euro infrastructure package will not be touched and is a done deal," Brzeski said. "All other measures, like the faster write-offs for investments or the corporate tax cuts in 2028 have become even more uncertain than before," he added, linking this to a now heightened risk of potential clashes over the country's budget.

Franziska Palmas, senior Europe economist at Capital Economics, also sees the fiscal package being implemented as planned.

"We think that will give a significant boost to GDP growth and get Germany out of stagnation after six years," Palmas told CNBC — but noted that due to the apparent dissatisfaction within parts of the coalition's factions, risks of such a boost being smaller or taking more time have risen.

Another key issue affected by Tuesday's turmoil is trust within the coalition — and that could prove vital for the government's economic policy plans, according to Otto Fricke, former member of the Bundestag for the Free Democratic Party.

"The problem really here is at the end, it's about the most important issue in politics: trust," he said, speaking to CNBC's "Europe Early Edition" on Wednesday. Germany's economy needs changes, and fast, if the goal is for it to grow, Fricke said.

"Therefore, you need trust within the cabinet, within the parliament, to do the legislation fast."

Capital Economics' Palmas pointed to Merz's vows that his government would be more stable than the previous one, which ultimately fell apart over disagreements about economic and fiscal matters.

After the tricky start to his term, however, "the risk that he will not be able to deliver on his promise that he will run a much more efficient and conflict-free government compared to the previous traffic-light coalition has risen," she said.

But despite the apparent tensions and increased instability, Hamburg Commercial Bank's de La Rubia meanwhile pointed out that, as highlighted by their joint coalition agreement, the CDU/CSU and SPD are in fact not that far apart politically.

For example, everyone should be able to agree on the need for investing in railways, roads, bridges and other infrastructure through the fund, and consensus on defense spending should also be found without "bitter conflicts," he said.

So, while Merz's first round failure on Tuesday may have been an attempt from members of parliament to teach him a lesson, it should not mean that the new government shies away from big change, de la Rubia said.

"It does not mean and it must not mean that they have to refrain from doing the necessary reforms with respect to modernizing the infrastructure, to reduce red tape especially when it comes to approval processes for construction work, wind farms, and electricity grids, improve digitalization processes and take the measures to reduce labor shortage," he said.

"I have few doubts about that the new government will be able to implement it's big policy goals"