Note that the perjury statute applicable to grand jury testimony provides this exemption:

(d) Where, in the same continuous court or grand jury proceeding in which a declaration is made, the person making the declaration admits such declaration to be false, such admission shall bar prosecution under this section if, at the time the admission is made, the declaration has not substantially affected the proceeding, or it has not become manifest that such falsity has been or will be exposed.

And it does not require there be two witnesses, as does the general perjury statute:

(e) Proof beyond a reasonable doubt under this section is sufficient for conviction. It shall not be necessary that such proof be made by any particular number of witnesses or by documentary or other type of evidence.

As to the general perjury statute, here is a quote from former President Clinton's rebuttal to possible perjury charges in Ken Starr's investigation:

The law is clear that in a perjury prosecution under 18 U.S.C. ' 1621, the falsity of a statement alleged to be perjurious cannot be established by the testimony of just one witness. This ancient common law rule, referred to as the "two-witness rule, " has survived repeated challenges to its legitimacy, and has been judicially recognized as the standard of proof for perjury prosecutions brought under ' 1621. See, e.g., Weiler v. United States, 323 U.S. 606, 608-610 (1945) (discussing the history and policy rationales of the two-witness rule); United States v. Chaplin, 25 F.3d 1373, 1377-78 (7th Cir. 1994) (two-witness rule applies to perjury prosecutions).

The U.S. Attorney's Manual compares the two perjury statutes here.