Coburn said, "The law clearly states felons convicted of abusing any health program are not entitled to further Medicare privileges."
"So I am very disappointed that, despite repeatedly raising the concern with Medicare officials, such felons continue to retain Medicare privileges," Coburn said. "A simple Internet search shows that Medicare officials have not instituted needed safeguards. This is a straightforward problem that Medicare's administrators can readily fix, but until they do so, the integrity of the program and the safety of patients will remain vulnerable to exploitation."
It's not uncommon for CMS to not meet a deadline imposed by a senator for response, according to Senate staffers who spoke to CNBC.com.
Noting that in the past "we have raised this issue of individuals being convicted of felonies and being able to still bill Medicare, and we have been told, 'Oh, we'll take a look at that,' " said one staffer, referring to CMS.
"We're always hearing that 'we're glad your concerned.' Now what are you going to do about it?"
Another staffer said that the failure to boot felonious doctors from the list isn't only a bureaucratic issue, it's also one that could affect the safety of patients.
"There's a real patient-care angle," that staffer said. "Doctors that have proven they don't regard the law as important, don't necessarily have patients' issues at heart."
The staffer also said that while there is "no silver-bullet solution to medical waste and fraud," kicking doctors off the list of people eligible for Medicare reimbursements when they're convicted of relevant crimes is much easier to tackle than some other issues.
(Read more: SHOP chopped! Online small-biz Obamacare enrollment delayed by year)
"This is kind of low-hanging fruit," the staffer said, noting the ease by which Carper's and Coburn's staffs were able to compile a list of convicted doctors who remained enrolled in Medicare. "If we can do this and point out the problem, then it's easy enough to fix."
Asked whether it was likely that there were many more doctors on the list, beyond the 21 the staff identified through public searches, that should have been bounced because they have been convicted of crimes, a staffer said, "Oh, absolutely. These are the ones that are public."
—By CNBC's Dan Mangan. Follow him on Twitter @_Dan Mangan