Could you elaborate on what's "extreme" about SYRIZA? Some of them have their roots in communist parties, but their actual politics today seem very close to the politics of most european social democratic parties 20-30 years ago.
They aren't talking about revolution, a dictatorship of the proletarians or anything like this, they just think that Greece should default rather than living on unsustainable credits forever, that the Greek tax code should be changed and that corruption should be reduced. What's "extreme" about that?
SYRIZA is extreme in that it appears not to live in a proper economic reality. They can not keep the promises they made in the election by forcing the EU to loan them money on Greece's terms. Anytime the EU gets sick of demands from Greece, the EU will simply turn off the flow of money to Greece and then Greece will collapse.
That's a reasonable criticism, but I think quite different from ideological extremism. Their problem, at least at the level of the leadership, is more just populism: they are telling Greeks many things that Greeks want to hear, which are mutually inconsistent. If anything the leadership lacks much of a hard ideological conviction, mixing together an eclectic combination of leftish economic sentiment with rightish nationalist sentiment, and a kind of paradoxical pro-EU/pro-euro position fitting uncomfortably with both of those. Hence there is this weird mixture of demanding German war reparations on the one hand (a completely counterproductive negotiating tactic purely for domestic nationalist consumption), trying to renegotiate the debt in a fairly technocratic/moderate way (into GDP-linked bonds) on the 2nd hand, a weirdly brash personal style on the 3rd hand which works badly with #2, a "red line" of no exiting the Euro on the 4th hand which restricts options considerably but is popular in Greece, and a bunch of electoral promises of the usual bread-and-wages kind on the 5th hand, which the combination of positions 1-4 leaves them virtually no room to actually enact. This all works very well for domestic politics, and the Syriza–ANEL coalition, a coalition of a large left-wing populist and a smaller right-wing populist party, is actually considerably more popular now than when they were elected. But it's not clear it is a winning strategy.
The actual left of Syriza has become very critical internally over that line, which they see as incoherent and not in tune with reality: in their view, the line Tsipras/Varoufakis are attempting to take just won't work, because it wants to promise staying in the Euro and then also a bunch of things that are incompatible with staying in the Euro, but won't admit that you need to pick one. Here is one interview with a left-wing Syriza MP, criticizing them along those lines: https://www.jacobinmag.com/2015/03/lapavitsas-varoufakis-gre.... You can differ over whether this line would be better, but I think it's more grounded in reality; Lapavitsas (the interview subject) imo much more clearly understands the concrete situation and what can and can't be done, and doesn't promise glibly that everything is simultaneously possible.
Basically the sovereign-country version of declaring bankruptcy, yes, except that it's messier because there is no bankruptcy court with jurisdiction to oversee it. You declare that you can't pay some or all of the outstanding debts, the creditors take a loss, your credit is ruined for the near-term future, some of it possibly ends up in various courts.
Alternately, you use the threat of that default to renegotiate the debt on more favorable terms. This also happens with personal bankruptcy, though the situations aren't quite analogous (some creditors will negotiate a more favorable repayment plan with debtors who seem like they might otherwise declare bankruptcy).
Unfortunately for Greece, afaict they have less leverage now than they did in 2010. At the time, much of their debt was held by German and French banks, so there was a mutually assured destruction angle. France/Germany would probably not sit by and let their large banks go down with the ship in the case of a Greek bankruptcy. So they would be forced to bail out the situation one way or the other, either bailing out Greece and thereby indirectly bailing out their banks by giving Greece money to pay them, or letting Greece default and then bailing out their banks directly. Now most of the debt has been moved to institutional holdings (the European Central Bank, IMF, etc.) as part of the bailout, which is less directly threatening. Probably Greece should've bargained harder at the time, but the previous government was a bit spineless.
Right now Grease gets more new loans / year than they pay out in interest payments. So their debt keeps growing until their next default / restructuring. It’s a vicious cycle.
On the other hand if they defaulted and did not need to make interest payments, but could not make new loans their cash flow would be worse off. But, they would have a reasonable path to long term prosperity by simply keeping their books balanced.
Of course there is always the 3rd option of defaulting and then trying to make new loans and default again. But their already getting free money from the EU so there is little point in doing this now.