From a DC Circuit opinion, (thanks Gabriel):

The deliberative process privilege is a qualified privilege and can be overcome by a sufficient showing of need. This need determination is to be made flexibly on a case-by-case, ad hoc basis. "[E]ach time [the deliberative process privilege] is asserted the district court must undertake a fresh balancing of the competing interests," taking into account factors such as "the relevance of the evidence," "the availability of other evidence," "the seriousness of the litigation," "the role of the government," and the "possibility of future timidity by government employees." In re Subpoena Served Upon the Comptroller of the Currency, 967 F.2d 630, 634 (D.C. Cir. 1992) (internal quotations omitted) (quoting In re Franklin Nat'l Bank Securities Litig., 478 F. Supp. 577, 583 (E.D.N.Y. 1979)); see also Tuite v. Henry, 98 F.2d 1411, 1417 (D.C. Cir. 1996) (describing need in the context of the law enforcement investigatory privilege, which involves balancing similar factors, as "an elastic concept"); Developments in the Law-- Privileged Communications, 98 Harv. L. Rev. 1450, 1621(1985) ("courts simply engage in an ad hoc balancing of the evidentiary need against the harm that may result from disclosure"); Larkin, supra, 5.03 at 5-89 to 5-92 ("need for [privileged materials] may vary considerably, depending on the circumstances"). For example, where there is reason to believe the documents sought may shed light on government misconduct, "the privilege is routinely denied," on the grounds that shielding internal government deliberations in this context does not serve "the public's interest in honest, effective government." Texaco Puerto Rico, Inc. v. Department of Consumer Affairs, 60 F.3d 867, 885 (1st Cir. 1995); see also In re Comptroller of the Currency, 967 F.2d at 634 ("the privilege may be overridden where necessary ... to 'shed light on alleged government malfeasance' ") (quoting Franklin Nat'l Bank, 478 F. Supp. at 582); Wetlaufer, supra, at 852 n.25, 855 (listing cases). . . .

If I was the lawyer for the Congress, in addition to hanging my hat on the powers of the Congress of oversight, I would use the bolded language above to strong effect if possible.