"We are not concerned about a near-term financial crisis in Italy, but we are concerned that Italy might face a serious debt crisis when we hit the next recession maybe in 2021, 2022," Carsten Hesse, European economist at Berenberg told CNBC's "Squawk Box Europe" on Friday.

The new deficit target is three times higher than the number that the previous government had planned. The higher public spending could spark negative market reactions, given that Rome holds the second highest debt pile in the euro zone — totalling 2.3 trillion euros ($2.67 trillion).

The leftist Five Star Movement and the right-wing Lega agreed Thursday night on a 2.4 percent deficit target for 2019 – despite opposition from some technocrat members in the government, including the finance minister, Giovanni Tria.

The two populist parties governing in Italy have come out looking victorious after weeks of intense cabinet discussions over next year's deficit.

The 2019 deficit figure could also raise problems with the European Union. Though the 2.4 percent target is still below the EU's threshold of 3 percent, it challenges previous demands from Brussels to lower its public debt pile.

There are also some concerns of potential slippages in the budget that would automatically increase the deficit.

"While the headline deficit figure may be sufficient for markets in the near-term, the focus will quickly turn to the details of the budget to see whether the deficit target is achievable," Mohammed Kazmi, portfolio manager at UBP private bank, told CNBC via email on Thursday.

"In addition, more medium-term questions around the sustainability of this government will remain given diverging views amongst coalition partners and the rise in support for (Deputy Prime Minister Matteo) Salvini which continues to provide him with an incentive to call for early elections if and when he sees fit," Kazmi added.

Salvini, who leads the right-wing Lega party, has gained public support since the appointment of the government, due to his strong stance on immigration policy.

A poll released this week by the SWG Institute (a market research company in Italy) showed that voters are increasingly supportive of the right-wing Lega and its leader Matteo Salvini. The party has risen to 32 percent of support from 17.4 percent at the election in March. On the other hand, the Five Star Movement has fallen to 28.7 percent from 32.7 percent in March.

Media reports suggested that both populist parties pressured the finance minister to increase spending in a way that their campaign promises were put forward. The same reports added that Tria could resign or be forced to resign otherwise.

"The risk is there (Tria's resignation)," Christoph Schon, executive director at Axioma, told CNBC's "Capital Connection" on Friday.

"But then again he has to be pragmatic about it. If he is going to resign: is it going to get better or should he try to find a solution?," Schon wondered.