Take Care Utah, a network of organizations that connects people to health insurance, can help, said director Randal Serr.
"We don't expect them to have the solutions. But we do," Serr said. "It involves a lot of calling, faxing and Internet usage … to get through these cases."
Those needing help can call 2-1-1 or go to the organization's website, takecareutah.org.
Undocumented immigrants are not eligible for health coverage, and probably do not account for many of the 4,300, said Jason Stevenson, communications director for the Utah Health Policy Project, which operates Take Care Utah.
Most of them are likely eligible but have not yet successfully conveyed their student, work or other visa information to the government or they've run into the glitches with the government website, he said.
Some citizens also have been told there are problems with their documentation, Stevenson and Serr said.
HHS said it has tried multiple times to reach each consumer who has documentation issues, using email, phone and mail in English and Spanish. Since May, it has closed 450,000 similar cases.
The new policy setting the Sept. 5 deadline affects the 36 states where the federal government runs the online insurance market created by the law. Utah ranked 16th among those states.
Hispanics, who historically have lagged in health insurance coverage, may account for a big share of the group.
Indeed, two states with large Latino populations top the list of unresolved cases. Florida has 93,800 cases, while Texas has 52,700. Georgia, Virginia and Pennsylvania round out the top five.
The Associated Press contributed to this story.