The complaint, first reported by The Washington Post and confirmed by ABC News, describes volunteers being told to prioritize procurement leads from conservative media personalities identified as part of a VIP list. These VIP tips on where to obtain protective gear were not more successful than other leads and consumed much of the group's time, according to the complaint.
"Americans are facing a crisis of tragic proportions and there is an urgent need for an effective, efficient and bold response," the complaint states.
"From my few weeks as a volunteer, I believe we are falling short. I am writing to alert my representatives of these challenges and to ask that they do everything possible to help front-line health-care workers and other Americans in need," the complaint adds.
Health care workers have faced a severe shortage of protective gear needed to respond to coronavirus, prompting the federal government to find new sources outside the U.S. Among the projects spearheaded by Kushner is "Project Airbridge," a program that uses taxpayer dollars to fly medical supplies from overseas on behalf of industry.
"This is an effort where the government is doing things that the government doesn't normally do, where we are stretching. We're acting very quickly," Kushner said at a press briefing in late April.
The details in the complaint, submitted last month to the House Committee on Oversight and Reform, were confirmed by the volunteer who spoke to ABC News on the condition of anonymity out of fear of retribution.
The committee declined to comment on the document.
According to the person who filed the complaint, the volunteers came from such firms as Welsh, Carson, Anderson & Stowe; Insight Partners; and McKinsey & Company.
"We applaud and support efforts to quickly bring medical supplies to states, territories, and tribal nations who desperately need them, but we are concerned by the Trump Administration's process for doing so, which appears to be -- at least in part --driven by politics rather than public health, and delegates decisions about distribution to private companies with little to no transparency about how distribution and pricing decisions are made," the senators wrote in their letters to the companies.
ABC News' Benjamin Siegel and Benjamin Gittleson contributed to this report.