You can't really compare the US to the Eurozone (and thus Greece) because while the US is both a monetary and fiscal union the Eurozone is merely monetary. While individual states in the US obviously have some level of fiscal autonomy the federal government still has a large amount of control over both taxes and spending. That's not the case in the Eurozone; the member countries are free to set their own tax and spending rates.
The issue with Greece (and Portual... and Spain... and Ireland... and to an extent Italy...) is one that was unfortunately inevitable as soon as the Eurozone was created. Those countries (generally known as the Latin/Southern Block or occasionally the PIGS) needed to have a weak currency to keep their economies flourishing. The so called Northern Block of the Eurozone, largely headed by Germany, needed a strong one. The Euro largely remained strong and, even before the series of financial issues that rocked the world, there was real tension there. As soon as the sovereign debt crisis hit? It came apart at the seams. Countries outside the Eurozone (the UK being a good example) could devalue their currency and put more of it into circulation to buy themselves time and soften the blow... Eurozone countries couldn't. Monetary but not fiscal union will never work. Different countries have different monetary needs... often wildly different. A crisis was inevitable. Sadly those who pointed this out were accused of being xenophobic, behind-the-times or (in the UK at least) "Little Englanders" and the voices on the left who had always opposed the European project were drowned out.
Here's the basic issue with Greece.
They have no money. They've spent it all.
Greece not only can't afford to support itself as-is, it also needs to pay back the groups it has already borrowed huge amounts from. Before anyone starts talking about vulture capitalists it's worth noting that those creditors have already agreed to write off 50% of the debt, accepted an interest rate far below what the open market would demand (open market Greek gilts are at around 15-25% depending on maturity, the rate Greece currently pays is 2.5%) and restructed the debt to give Greece longer to pay it off multiple times. For the record those are far, far, far more generous terms then Ireland, Spain or Portugal got during their own bailouts.
Let's also remember what the consequences would be of simply not paying back their debt and reneging on it. Who is going to lend to a country that refuses to honour its debts? Because of politics and the warped version of Keynesian economics (sometimes called the "new neoclassical synthesis") that currently dominates economic policies there are few if any countries that can actually support themselves without borrowing. But again, who'd lend to Greece if they have a history of not paying their debts? And even if they did agree to lend how high an interest rate would they demand to make up for that risk (which is the reason gilts are used to measure how strong a countries economy is; the less risk the lower the interest rate and vice-versa).
The truly tragic thing is even eight months ago this was all avoidable. Yes, the conditions of the bailout had been tough. Yes, they would be tough still. But GDP was up and employment was down as 2014 came to an end. A corner had been turned and while things were still going to be tough and still going to suck for a while the end of the bailout was in sight... just as it was with Ireland and Portugal. Then came the news of the snap election, then came the electoral upswing of Syriza who were talking about increasing spending (remembering that Greece already didn't have any money to spend) and refusing to pay debts. Understandably both the markets and other governments balked at this... especially countries like Ireland and Portgual that had suffered through the hard times, kept their word and paid back the money they owed and were now being asked to fund Greece refusing to do so. Thus the sad situation we face now.
So what happens next?
Frankly, it's hard to tell because the referendum didn't really mean anything. The Greek people were asked to vote on a deal that had already been taken off the table. It was symbolic at best. And the problem with symbolic gestures is that they mean nothing compared to the cold, hard, economic truth of life... much like how the symbolic gesture of a closer Europe was allowed to trump realities and thus cause the Eurozone in the first place.
We'll know more tomorrow when the Greek PM Alexis Tsipras addresses the leaders of the Eurozone. But both sides appear backed into a corner. Tsipras' rhetoric and the result of the referendum, symbolic or not, means he can hardly back down now. But neither can the powers that be in the Eurozone. A weakening of their position against Greece will bring the other countries who went through bailouts screaming that they deserve reperations for not getting as sweet a deal (and as above the Greeks already have the sweetest deal of them all). And in Spain's case with an election coming up their leader, under pressure from a Syriza type party back home, isn't going to want to give them anything.
Personally I think Greece has to leave the Eurozone... and the quicker the better. It should never have been there to begin with... both in technical terms (it failed all the entry tests) and in judgement (it was always going to suck for them). Then it can devalue and while things will still be awful there's a way out. The current zombie-state existence where Greece is only kept alive by other people throwing them money can't go on. It hurts everyone. The question is having already sacrificed so much to the vanity of the Eurozone whether politicians are willing to finally let it tumble or whether they'll drag this out.
And Greece has to get itself in order... even before the crisis it had a real tax and spending problem. Tax evasion is a huge issue... and for once it's not the super rich doing so but the professional middle-classes. There's a very interesting paper on it here
but the headline example is this; professional Greeks self-reporting their taxes claimed that they spent more money servicing consumer debt then they made in a year. For comparison even in countries considered to have huge consumer debt the figure is around 30%... and that's the very upper bracket. That 100%+ figure doesn't come about because Greek doctors or lawyers were bouncing from pay day loan to pay day loan... it's because they were massively under-reporting their income so they could avoid taxes.
On the spending side of things there was what was assumed to be an apocryphal story about the Greek train system being so under-used and over-subsidized that it would be cheaper to make everyone who uses it get a taxi instead. Turns out it's pretty much true
as long as three people share each taxi. Now in reality it's not quite as simple as just cancelling all trains and paying for taxis instead... much of the cost of the rail network comes from the generous pensions and the like which were funded with debt spending... but it's a simple example of what went wrong with Greece. They spent far too much money, got far too little back in tax and without control over their monetary policy simply couldn't do anything to sort it out when the good times ended and the bad times rolled in.
I think Greek people are scared... and who can blame them. And they're proud... and again, who can blame them for that? That's why they said no at the referendum. I'm not sure anyone ever won the hearts and minds of a people by saying that they'd have to pay more taxes and have their services and benefits cut. The hope Syriza offers that all debts will be cancelled and that spending can be increased may be completely illusory... but it's hope none the less. And with banks literally running out of money, food being horded, pensions quite possibly soon not being paid and medicine not be available hope is a tempting answer.