More: It is unclear who will replace former BLS Commissioner Erika McEntarfer. Still, any signs that lead investors to suspect data is being politicized could exacerbate concerns about CPI data collection.

In that case, investors are likely to demand higher compensation to hold TIPS, or Treasury Inflation-Protected Securities, whose value is linked to the CPI, and raise the federal government's cost of funding itself, analysts said. Rises in TIPS yields could be exacerbated by poorer liquidity compared to the much larger market for nominal Treasuries.

"This isn't just an academic discussion about getting the right numbers - these numbers matter for TIPS," said Michael Feroli, chief U.S. economist at JPMorgan Chase. "There's real money on the line here."