Would the U.S. auto industry be doing as well as it is today if it was Mitt Romney completing his first term as president?

Romney argues that his plan for the industry in his now-famous November 2008 New York Times op-ed piece, "Let Detroit go bankrupt," was what the Obama administration eventually did: a managed bankruptcy at both companies. He insists that he was not in favor of the companies going out of business.

But in the 2008 piece, Romney said the money needed to keep General Motors (GM) and Chrysler Group alive during bankruptcy should have come from the private sector, with the government providing only "guarantees for post-bankruptcy financing." Those guarantees would have made lenders whole if the automakers subsequently defaulted.

The problem was that there was no one available to write checks for the automakers other than the government in late 2008 and early 2009.

The financial markets had melted down in the wake of the Lehman Brothers bankruptcy. Treasury was pumping billions into the nation's banks, who were not willing to then lend money to a struggling auto industry -- or anyone else.

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Steve Rattner, the Obama administration car czar at the time, said in his own New York Times op-ed piece that the administration tried to find private financing, but that "not one (would-be lender) had the slightest interest in financing those companies on any terms."

Rattner told CNNMoney on Tuesday that the administration never tried offering loan guarantees.

"If the government was going to be on the hook one way or another, we did not see the point in bringing in a private party," he said.

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Bob Lutz, the vice chairman of GM at the time and an outspoken Republican himself, said the loan guarantees Romney talks about would not have made a difference due to the cash crunch at the time.

"The banks were even more broke than we were. Who had the money?" he told the Detroit Free Press in February. "Loan guarantees don't do any good if the banks don't have any money."

Without financing, both companies would have had to close. And even if they had survived, they could be struggling today rather than reporting record profits and strong sales. Many of their suppliers would have also been forced to shut down, and that could have caused bankruptcies at other automakers such as Ford Motor (F), which would have been unable to build cars without their supplier base.

Lutz said Tuesday that the government was the only one willing to give GM most of the help it needed in return for stock in the company, rather than heaping on more debt that it couldn't afford. Even the Obama administration was reluctant to do that, Lutz said. But it was the only way a healthy GM could emerge from bankruptcy.

"Why perpetuate the problem with $53 billion of new debt, at an annual interest cost of, say, $3 billion?," Lutz said. Private financing would have left GM with "enough debt to wreck the future of a recovering GM."

In Monday's third presidential debate, Romney made clear he still opposes the $60 billion in direct help the automakers received from Treasury.

"My plan to get the industry on its feet when it was in real trouble was not to start writing checks. It was President Bush that wrote the first checks. I disagree with that," he said.