And that's just the start. Ahead of this week's meeting of the ECB governing board there is a Latin summit in Madrid between the two men -- Italian Prime Minister Mario Monti and his Spanish counterpart Mariano Rajoy -- in the hottest seats.
"I don't want to raise expectations but I must say that we have arrived at a decisive point," said eurogroup President Jean-Claude Juncker. "The euro countries have arrived a point where we must make extremely clear with all available means that we are determined to ensure the financial stability of the currency union."
"All available means" now joins Draghi's "Whatever it takes" as key phrases propping up the skeptical markets. But the markets expect a very large rabbit to be conjured out of the ECB's hat this week. We don't know what it will look like but we do know what it won't be.
We know from the ECB, which has issued a legal opinion saying it cannot be done, that it cannot be a banking license for the new bailout fund, the European Stability Mechanism, which might have enabled it to swell its war chest by raising money in the markets.
We know from the German Bundesbank that they aren't prepared to swallow any more ECB purchases of the stricken bonds of Italy and Spain. Since those two countries alone need some $1.3 trillion in new and rollover debt over the next three years, the markets will have to be persuaded that somebody reliable stands behind that debt.
But "reliable" is no longer a word that people associate with the euro, after private bondholders of Greek debt were forced to take a haircut in the last "rescue" package. And now the Greeks need another one and officials in Brussels and at various central banks have been conferring over the weekend whether this time they too should be prepared to suffer haircuts.
What we don't know is whatever new notion Geithner may have taken from Washington, where the Obama administration's mind is focused tightly on the effect of a euro crash on the U.S. economy and thus on Barack Obama's re-election.
We know how seriously some of the key Washington institutions are taking this, particularly the International Monetary Fund which has just warned: "the euro area crisis has reached a new and critical stage ... raising questions about the viability of the monetary union itself. The adverse links between sovereigns, banks and the real economy are stronger than ever."
The mood of the markets, faced with the nightmare of a disorderly euro collapse, is hard to read. An implosion of the euro would probably spark a panic and a global depression. But the slow crumbling the euro now suffers is almost as bad.
The markets, depressed by the pitiful series of half-measures the eurozone leaders have cobbled together in the past, are listening to their own gurus, like Citibank's Willem Buiter, who says Greece will be forced out of the euro within months and both Spain and Italy will by the end of this year be in the hands of the IMF's rescue mechanism. Jacques Cailloux from Nomura says that Rome and Madrid will need a rescue "within weeks."
The markets will also be looking at the latest gloomy reaction of German public opinion. More than half of those polled say their country would be better off out of the euro, a poll published Sunday by the daily Bild indicated. More than 71 percent of respondents said that Greece must leave the euro if it didn't live up to its austerity promises and only 29 percent said the German economy would suffer if it was to leave the common currency.
Greece's fate rests with a small team of inspectors from the EU Commission, the ECB and the IMF, who are deciding whether the Greeks have kept enough of their promises of austerity to qualify for the next tranche of aid. The signs aren't good.
On his arrival in Greece last week, EU Commission President Jose-Marie Barroso warned: "To maintain the trust of European and international partners, the delays must end. Words are not enough. Actions are much more important. The key word here is: deliver. Deliver, deliver, deliver."
Whether the Greeks can deliver is another question. Tourism is its biggest industry, delivering 17 percent of Greece's economy and employing one Greek in five, and the Bank of Greece has just reported that tourism this year is down 11 percent. And there isn't much Tim Geithner can do about that.