AP/Jim Cole
"Greece will happen here if we do not change course. Anyone who disagrees with this is a 'math denier,'" Jindal said in a statement on Monday.
The governor's comments come as Greece is set to default on its debt, which sent stocks plummeting and threatened Greece's status in the Eurozone.
Jindal said that President Barack Obama's spending record is putting the US on a path to financial instability, and that a 2016 victory for Hillary Clinton would virtually ensure a crisis.
"This is the American future if we continue going down the road that President Obama has us on, and that Hillary Clinton wants to continue and even accelerate," Jindal said.
"Greece is now coming to the pot of gold that awaits at the end of the socialist rainbow, and Hillary Clinton pledges to take America further down the road to socialism," Jindal said.
Jindal's argument is similar to the argument that former Massachusetts Gov. and Republican presidential nominee Mitt Romney (R) made in 2012 when it became apparent that Greece needed another bailout to manage its debts.
But though Romney and now Jindal appear to be making a point about excessive government spending and debt, the comparison is flawed.
That's because US debt and Greek debt are nothing alike.
Greece owes money to its creditors in a currency that it does not control. The International Monetary Fund, the European Commission, and the European Central Bank have bailed out Greece several times and set the terms for how Greece pays back its debt. Greece has no way to pay back its debt other than to accept austerity measures imposed by these three groups.
In contrast, the US is has a currency it controls and risks no debt default. And its debt is denominated in dollars.
As The Atlantic notes, if a debt situation got particularly bad in the US, America could technically print its own money to pay back its debt, since it owes money in a currency that it controls. This would increase inflation and weaken confidence in the dollar, but wouldn't spell doom for the US economy.
Myles Udland contributed to this report.