At this early stage of the 2016 presidential race, when no politician has yet declared his or her candidacy, Sen. Rand Paul (R-Ky.) is benefiting from an awful lot of buzz. And in a recent poll of New Hampshire, he trailed only New Jersey Gov. Chris Christie.

As a potential candidate, every interview Paul gives from now on will be parsed with an eye toward 2016. And yesterday, he talked with Bloomberg's Joshua Green to discuss Washington and the policies behind his "libertarian populism."

So how did he do? Columnists on the left (and at least one on the right) think Paul's performance was pretty subpar. Here are three signs that he may not quite be ready for primetime.

1. His case for gutting the budget leaves much to be desired

Green asked Paul about an article that claims his budget would eliminate the State, Energy, and Commerce Departments, as well as the Environmental Protection Agency and the Food and Drug Administration.

"Many Americans who have suffered during a recession have had to cut their spending 1 percent, and they didn't like doing it, but they were able to do it to get their family's finances back in order," Paul replied. "I see no reason why government can't cut 1 percent of its spending."

While folksy, equating massive budget cuts to simple household budgeting isn't particularly illuminating, argues The Washington Post's Ezra Klein:

So that's not actually an answer. Paul's budget eliminates the Department of Commerce. It also eliminates the Department of Education. And the Department for Housing and Urban Development. And the Department of Energy. The State Department gets cut by more than 50 percent.

Meanwhile, it increases spending on defense by $126 billion. Perhaps these are good ideas! But Paul doesn't defend them. He obscures them. [The Washington Post]

2. He's warning of a phantom trillion-dollar deficit

Later, to justify those proposed cuts, Paul cited "a trillion-dollar deficit every year," saying, "I mean, that's an extremely bad situation."

But there is no trillion-dollar deficit, says Paul Krugman of The New York Times, who puts the number at "$600 billion and falling fast."

"I think it's pretty clear that Paul actually has no idea that the deficit is falling," Krugman writes, adding:

The whole incident reminds me of 2011, when supposedly well-informed candidates like Tim Pawlenty went on about soaring government employment during a time of unprecedented cuts in the public payroll. Once you're inside the closed conservative information loop, you know lots of things that aren't so. [The New York Times]

3. He's joking about picking dead economists to head the Fed

Paul wants to shutter the Federal reserve. And he made that point with a joke:

Who would your ideal Fed chairman be?

Hayek would be good, but he's deceased.

Nondead Fed chairman.

Friedman would probably be pretty good, too, and he's not an Austrian, but he would be better than what we have.

Dead, too.

Yeah. Let's just go with dead, because then you probably really wouldn't have much of a functioning Federal Reserve. [Bloomberg]

Ross Douthat, conservative columnist for The New York Times, is not amused:

What Rand Paul says about his budget and the Fed here are basically libertarian populism's weaknesses in a nutshell: http://t.co/rKWB2cRYLk — Ross Douthat (@DouthatNYT) August 9, 2013

New York's liberal columnist Jonathan Chait also takes issue with Paul's stance:

Paul is a hard-money fanatic who wants to abolish the Federal Reserve's role in using money policy to stabilize the economy. That's the joke. Milton Friedman, though, had the complete opposite view of monetary policy. His central academic insight was support for very active monetary policy. He called it 'Monetarism.' Look it up! [New York Magazine]