DETROIT — Auto sales are growing so fast that Detroit can barely keep up.

Three years after the U.S. auto industry nearly collapsed, sales of cars and trucks are surging. Sales could exceed 14 million this year, above last year’s 12.8 million.

The result: Carmakers are adding shifts and hiring thousands of workers around the country. Carmakers and parts companies added more than 38,000 jobs last year, reaching a total of 717,000. And automakers have announced plans to add another 13,000 this year, mostly on night shifts.

But there’s a downside. The newfound success is straining the factory network of the Detroit automakers, as well as the companies that make the thousands of parts that go into each vehicle. This could lead to shortages that drive up prices.

And it also has auto executives in a quandary. They got into trouble in the first place largely because their costs were too high. Now, they fear adding too many workers.

Ford, for instance, is “squeezing every last component, transmission, engine out of the existing brick and mortar,” says Jim Tetreault, vice president of North America manufacturing.

Still, the surge in hiring bolsters the argument of those who supported the federal bailout of General Motors and Chrysler in 2008. The bailout has been a major issue in the days leading up to today’s Michigan Republican Party primary. GOP front runner Mitt Romney opposed the bailout, which was supported by then-President George W. Bush and later by President Barack Obama.

And the hiring is good news for communities around the country that saw hundreds of thousands of manufacturing jobs disappear. Starting in 2005, GM, Ford and Chrysler closed 28 factories and eliminated 88,000 jobs. Parts companies cut another 234,000.

Now, if sales hit 15 million by 2015, as some experts predict, the three Detroit automakers could hire another 20,000 people, predicts Sean McAlinden, chief economist for the Center for Automotive Research in Ann Arbor, Mich.

“You can only squeeze so much out of the same amount of people,” says Itay Michaeli, an auto analyst at Citi Investment Research.

Laurie Schmald Moncrieff, president of a small parts-manufacturing company near Flint, Mich., says when demand for auto parts collapsed, she shifted production to parts for companies in green energy, aerospace and defense.

Now, automakers and other parts suppliers have her on speed dial, trying to line up everything from fuel pump parts to tools that make hoses. She just added six workers and may hire another five. “I see tremendous growth coming in the near-term,” she says.

Yet like many parts suppliers, she’s having trouble finding people with the skills to run machinery in her plant.

The hiring binge couldn’t have happened at a better time for Michigan. Many of the new auto jobs came around the Great Lakes where the Detroit Three have most of their factories. New jobs with auto companies don’t pay as well as the old ones. Under union contracts, companies can pay new hires around $16 per hour, a little more than half the pay of longtime workers.

But in a state where unemployment was above 14 percent just three years ago, any jobs are welcome. And Michigan is not the only region to benefit. Ford is adding positions in Louisville, Ky., Chicago and near Kansas City, Mo. Chrysler is adding jobs in Belvidere, Ill., and General Motors is hiring at plants in Tennessee, Kentucky, Texas and New York.