Democratic strategist James Carville’s brash advice for President Obama – “fire a lot of people” – has raised some eyebrows in Washington, and with it the question of whether he could be right.

“It’s not going to work with the same team, the same strategy and the same excuses,” Carville said in an open letter to Obama posted on CNN.com. “It’s time to show them the exit. Wake up — show us you are doing something.”

Carville, who has advised the presidential campaigns of Bill and Hilary Clinton and Sen. John Kerry, hasn’t been bashful about criticizing the Obama White House.  But his latest prescription – “panic!” – ups the ante just a little bit more.

Obama needs to take a page from the playbooks of Clinton and Reagan, who both revitalized their political standing at points during their presidencies by shuffling their staffs and throwing some members out the door, Carville said.

But history also offers examples of presidential purges gone awry.

Princeton University presidential historian Julian Zelizer said Presidents Gerald Ford and Jimmy Carter both deeply undermined their credibility to govern after making similar moves.

When Ford shook up his cabinet and rearranged his staff in 1975, “it backfired,” Zelizer said. “I looked like Ford was losing control and not gaining control.”

Four years later, Jimmy Carter’s “great purge” – ousting 34 cabinet members and staff aides – met a similar fate. 

“It looked like he was out of control and didn’t know what he was doing, as it were,” Zelizer said.

“I think it’s very hard to play out politically what’s the public going to think of a shake-up. So I don’t know if Carville is right about the political consequences,” he said.

One potential concern for Obama could be that cleaning house would publicly confirm that something is wrong with his approach on the economy — an admission neither he nor his aides have been willing to make.

Obama has devoutly affirmed his policy, while asking for patience – and an end to partisanship – to see it through.

“We are going through extraordinary times,” Obama told a crowd of donors at a private Washington, D.C., fundraiser Thursday night. “Historically, after financial recessions, it is a challenge and a struggle.  And over the last two and a half years what we’ve been able to do is stabilize an economy, but at a level where unemployment remains way too high.”

That fact won’t disappear soon, staff shake-up or not. And it’s something many Democrats point to in suggesting Obama’s strategy has got to change.

“I think it’s up to the president right now … to make clear what he stated the other day – that he’s going to get up and think about jobs, [that] there’s a sense of urgency and commitment,” said Andy Stern, the former president of Service Employees International Union, “and he’s not going to just sit around and referee, you know, disagreement between the two political parties.”

ABC News’ Jon Garcia contributed to this report.