The question of limiting subsidies to some states is the key issue in a Supreme Court case.
They warned they will "strongly object to any effort to politicize" the CBO.
Conservative groups are pushing GOP leaders to replace Doug Elmendorf.
Doug Elmendorf has been in the middle of a series of political storms this year.
The agency said it began the process of expanding its current policy late last year.
Analysts with contrasting ideologies say Doug Elmendorf should remain CBO chief.
Peter Orszag urged Republicans to reappoint current CBO Director Douglas Elmendorf.
The CBO's director told lawmakers that disincentives would cut into the labor supply.