See JakeS:

But a couple of years ago, before the crisis, Italy suggested using its own central bank to run its own monetary policy. The ECB threatened to stop clearing payments with the Italian central bank if they did so, and the Italians backed down.

Also:

A swedish kind of death:

European Tribune - Beggars can't be choosers

However the ECB could turn off the liquidity taps to the Irish Banks at any time thus effectively bankrupting them whatever the Irish Government might do.

Can it? How would it work?

If yes, could not the Irish government issue scrip in such a situation?

Migeru:

In that case the Irish banks would be insolvent and would have to be intervened by their regulator or national deposit insurance scheme. The assumption would be that the Irish government doesn't have enought cash even for a "Good Bank" resolution of its banks.

JakeS:

But that is ridiculous. Surely they have enough liquid assets to cover all domestic depositors?

Migeru:

After all we've seen in the last 3 years, I wouldn't bet my life savings on that surely...

Buiter in his paper on Central Bank insolvency does discuss the fact that the Central Bank can always make itself solvent assuming the liabilities of the economy are denominated in its own currency and not index-linked by seigniorage but sometimes at the cost of unacceptable inflation rates. So, effectively it is possible for a central bank/treasury combination to be jointly insolvent. Is that the case in Ireland? In fact, in the document linked to by afew: upthread

Buiter, who comments rarely now he works for Citi... Brought this out the other day:

Sovereign Debt Crisis Update (pdf).

Buiter claims

Accessing external sources of funds will not mark the end of Ireland's troubles. The reason is that, in our view, the consolidated Irish sovereign and Irish domestic financial system is de facto insolvent. The Irish sovereign cannot from its own resources `bail out' the banks and make its own creditors whole. In addition, a fully-fledged bailout (permanent fiscal transfer) from EA partners or the ECB is most unlikely. Therefore, either the unsecured non-guaranteed creditors of the banks, and/or the creditors of the sovereign may eventually have to accept a restructuring with an NPV haircut, even if it is not a condition for accessing the EFSF or the EFSM at present.

Of all the ways of organizing banking, the worst is the one we have today — Mervyn King, 25 October 2010