In theory.They don’t need to. The reason America has such crushing debt is because the republicans keep cutting taxes for their 1% backers but are still finding they need to spend a shedload of money in keeping the state functional.
The EU is actually a better system than the USA because each country is still its own separate jurisdiction of laws, taxes and so on. The EU is just a large area of some common laws (eg don’t destroy the environment) with freedom of movement of capital, trade and people across borders.
It’s not as federalised as the USA by a long shot.
But in practice, the EU laws can be used by some countries for their own benefits and create a disadvantage to other countries.
For example, the price of electricity is indexed to price of gas.
When the gas price rose, electricity providers in France were forced to sell the cheap electricity they produced and buy back at a high price. French citizens had to pay huge electricity bills even though France has plenty of nuclear power plants that produce cheap electricity.
The EU is not just an agreement for trade between countries. EU laws are hierarchically superior to national laws.
Every country in the Euro zone is forced to follow ECB policy even if it doesn't benefit to them. This raises questions about sovereignty.