Italy's situation appears the most complicated.
But Italy's economy is now forecast to grow this year by only a small fraction of the 1% assumed in late 2018.
If they are considered insufficient, the Commission will start disciplinary action that could end in a fine of 0.2 percent of Italy's GDP - around 3.5 billion euros ($3.9 billion)- if Rome repeatedly ignores European Union calls to put its finances on a sustainable track.
The opening of such a procedure, which needs to be validated by European Union finance ministers, could result in financial sanctions of up to 0.2 percent of Italian GDP, which corresponds to the three billion euros mentioned by Salvini.
Although the numbers seem damning for Italy, EU rules give the Commission a broad margin of discretion when it issues its assessment on June 5. "But any potential compromise in regard to the 2020 budget will run against the government's spending plans".
That is in contrast with a compromise struck with Rome late previous year, under which Italy was exceptionally allowed to keep its structural deficit unchanged, instead of reducing it, with a marginal easing in debt in 2019, based on an optimistic economic growth assumption. Hardline Interior Minister Matteo Salvini's League party - who is casting himself as the standard bearer for populist far right in Europe - won the Italian vote and jumps from 6 to 28 seats in the European Parliament.
A key policy the leader of the League party wants to introduce is a flat tax measure that critics would say will increase the deficit further.
"The commissioners no longer have to worry about how a hard topic like this will affect their election prospects", he said in an interview.
"Salvini will feel emboldened by the election results and so he will face the problem of pushing for his political priorities while the government will seek to keep the deficit within acceptable limits", the professor said.