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By Jon Schuppe

President Obama pledged Wednesday to cover "all of the people of Flint's backs" as the Michigan city struggles with the pollution of its drinking water.

Speaking in nearby Detroit, Obama digressed briefly from remarks on the auto industry to share his outrage with the unfolding crisis, in which lead has leached into the water piped into thousands of Flint homes.

"I know that if I was a parent up there, I would be beside myself that my kids' health could be at risk," Obama said.

Obama declared a state of emergency in Flint on Saturday, allowing the Federal Emergency Management Agency to deliver bottled water, water filters and home test kits, a supplement to local efforts already underway.

And the president's visit to Michigan came a day after Gov. Rick Snyder apologized in his State of the State speech for his handling of the crisis, which has been unfolding since the city switched its drinking water source to the Flint River to save money in April 2014. That fateful move came under the leadership of an emergency city manager appointed by Snyder.

Back when the water supply was swapped, Residents immediately began complaining about the taste, smell and appearance of the water, but officials said the water was safe. Tests later found elevated lead levels in the blood of local children — the result of an insufficient treatment process that left the water highly corrosive, causing lead to leach from pipes.

Related: Bad Decisions, Broken Promises: A Timeline of the Flint Water Crisis

Snyder on Tuesday asked the state legislature for a special allocation of 28 million to help Flint get through the next few weeks.

Flint Mayor Karen Weaver, who took office last fall, visited the White House on Tuesday. She and Obama discussed the crisis.

"I told her I'd have her back — and all the people of Flint's backs as they work their way through this terrible tragedy," Obama told the auto workers.

The Flint River.Bill Pugliano / Getty Images

Weaver stayed in Washington Wednesday to take part in a news conference with the U.S. Conference of Mayors, where she said the impoverished city of 100,000 needed more money and resources.

"I don't know at what point we'll be able to drink the water yet," she said.