The referendum result makes life even more challenging for Italy's banks, after the country voted against Prime Minister Matteo Renzi's proposed constitutional reforms.
Several banks are trying to raise new money from investors to reinforce their financial foundations.
Attention is focused especially on Banca Monte dei Paschi di Siena, Italy's third largest bank and the world's oldest. It came out of a recent European Central Bank assessment worse than any other major lender.
Italy's banks are currently one of the main trouble spots for the eurozone.
They are struggling with a burden of bad debt, loans that are unlikely ever to be repaid fully.
So they are trying to unload some of these loans - sell them to investors that specialise in dealing with problem debt. Some, including Monte dei Paschi di Siena are also trying to raise new capital, to strengthen their financial foundations so they can better cope with losses on problem loans.
The banks are a potential flashpoint in an economy that has for some time been seen as potentially posing wider risks to the EU's currency area.
However, it is the size of the Italian economy and the size of the government debt that makes the country a smouldering financial volcano. The risks are aggravated by the political situation.
Italy is the third largest economy in the eurozone. The government debt burden, depending on which figures you look at, is certainly one of the largest in the eurozone. In fact, on one measure its debt burden is the largest. As a percentage of the national economy, or GDP, it's an eye-watering 133%, second only to Greece in Europe.
One of the roots of the problem is Italy's two decades of dismal economic performance. Measured by total economic activity (gross domestic product, or GDP), the economy remains about 8% smaller than it was at the onset of the international financial crisis.
It is roughly the same size as it was at the turn of the century.
That has made it harder to generate the tax revenue needed to keep the government's debt burden down. It has also increased the chances of businesses getting into difficulty and being unable to maintain their loan payments.
The result: Italian banks are weighed down with a massive problem of bad debts, or non-performing loans (NPLs), worth €360bn (£307bn), equivalent to about a fifth of the size of country's economy.
The problem has been exacerbated by the country's bankruptcy legislation, which made it very slow for lenders to get their money back when a borrower has failed financially. The law has been changed under the government of Matteo Renzi, but it has taken time to make itself felt in practice.
One way that banks can deal with problem loans is to sell them to other investors. But the delays in the foreclosure procedures that enable creditors to recover the money mean these deals involve deep discounts.
That, in turn, would mean the banks would have to acknowledge heavy losses in their accounts, further undermining their financial foundations.
At best, the NPL problem inhibits the banks' ability to provide the new credit that Italian businesses need to generate a more convincing economic recovery.
At worst, there is a risk that the failure of a large bank could set off a wider financial crisis and set the recovery back more severely.
Banca Monte dei Paschi di Siena is at the centre of this crisis. Its shares have lost more than 80% of their value this year. It has been ordered by the European Central Bank to reduce its holdings of bad debt.
The bank is trying to raise new capital to the tune of €5bn, and plans to do it by issuing new shares and by asking some creditors to convert the debts they are owed into shares.
Several other banks have problems too.
The referendum plays into this problem simply because repairing the banks is more difficult in the face of profound political uncertainty. The worry is, will investors want to put their money into a struggling lender when the political environment is so hard to read?
Mr Renzi has announced his resignation and Italy's president will decide later whether to appoint a new PM or hold elections.
The Five Star Movement, which headed the No campaign in the referendum, is anti-euro, although that does not mean that a eurozone exit is now on the horizon.
There are many steps that would have to be taken first, and in any case European Commission surveys have consistently suggested Italian public opinion favours sticking with the currency.
One option that has been considered for the banks is a bailout by the Italian government. There are two problems with that: one financial and one legal.
The financial issue is that the Italian government's dismal finances mean it really doesn't need the additional burden of propping up the banks.
The legal point is that European Union rules, agreed in the wake of the financial crisis, require a bank's creditors, in particular its bondholders, to take losses before the taxpayer steps in.
It's an approach that can make sense. Bondholders are usually professional investors who can handle losses and are also, in theory, better able to monitor banks and discourage them from taking excessive risks in the first place.
Monitoring the markets
But in the case of Italy, many of these bonds are owned by retail investors. So, following the EU rules and imposing losses on this group would be very unpopular in Italy and many would say unfair.
The rules are part of a very important project in the eurozone, called banking union. It was a response to the region's financial crisis, intended to make the banks more resilient and to break the malign link between weak banks and financially stressed governments.
So far the impact of the latest political turn of events on the Italian government's borrowing costs in the financial markets has been unfavourable but very moderate. It would have to pay an interest rate of about 2% to borrow for 10 years. When the crisis was at its worst five years ago the figure was more than 7%.
If the situation were to deteriorate, the European Central Bank has some scope to help - though there are limits - by increasing its purchases of Italian government bonds or debts under its quantitative easing programme.
So far though, it has not been needed as the markets don't appear to think that the outlook for the Italian government's financial position has deteriorated very much.