By Phil LeBeau, CNBC Correspondent

As the President takes a bow in Detroit after his administration saved the Big 3, the real story in Michigan is whether the folks who run GM and Chrysler (and many of the suppliers) will remember how close they came to collapsing.

They had better not forget.

Not because taxpayers pumped more than $50 billion into saving GM and Chrysler, but because Detroit has a poor track record of repeating its mistakes.

Remember when buying a Big 3 car meant buying big headaches? I do. Fortunately, in the last 10 years Ford ( F), GM and Chrysler have learned from their mistakes and started making quality a true priority. But now is not the time for them to think they've caught up.

There's still more they can do to improve.

Remember when GM ran up massive debts and couldn't cut its costs quick enough? I do. Sure, its post-bankruptcy debt is manageable, but it needs to be vigorous in making sure it doesn't slide into its old habits. Ed Whitacre and Chris Liddell are adamant that this is a more fiscally prudent General Motors. Here's hoping those who are carryovers from the old GM adopt that same attitude.

Remember when Chrysler let its pipeline go bone dry under the ownership of Cerberus Capital? Who can forget? It's no wonder Sergio Marchionne and Fiat got Chrysler for a song. I hope Chrysler's rank and file never again have to go through what they did in the last three years. If they do, their company likely won't survive.

Remember when GM and Chrysler were about to collapse last year, and line workers would say to reporters, "Give us a chance, we'll make America proud." I won't forget because I heard it time and again. When labor contracts come up in 2011 and shortly after that, let's hope the rank and file remember their pledge to work together with automakers and avoid the saber rattling that marked years of contentious labor negotiations.

Bottom line: The Big 3 have a unique opportunity to win over American car buyers. Ford is proving that a Detroit automaker can re-make itself. GM and Chrysler are trying to do the same. And that is the most important message to take away from President Obama's visit on Friday.
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