White House Coronavirus Task Force Coordinator, Doctor Deborah Birx, named the city in a recent private phone call.
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Audio of the call was obtained by the Center for Public Integrity.
However, other than the audio, the center does not include San Jose in their reporting.
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Mayor Sam Liccardo says he's never had any contact from the White House about test rates.
In a statement, the county of Santa Clara said the increase in cases in all these cities demonstrates the need for a coordinated national approach to the pandemic.
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