Veterans Educational Opportunities Enhancement Act of 2001

Allows the withdrawal of an election not to receive such assistance during a specified open period for an individual who: (1) first becomes a member or enters into active service on or after the enactment of this Act; (2) continues to serve the period of obligated service without a service break; (3) before completing such period, is discharged or released from duty for a service-connected disability, a preexisting medical condition, a hardship, a physical or mental condition that did not result from the individual's own willful misconduct, or for the convenience of the Government; (4) completes the requirements of a secondary school diploma or equivalency certificate or 12 semester hours toward a standard college degree; and (5) is discharged honorably or placed on one of specified retirement lists. Provides a basic pay reduction for entitlement to such assistance.

Provides an opportunity for certain active-duty military personnel who first became a member of the armed forces before July 1, 1985, to enroll for such assistance during an open period under eligibility requirements very similar to those above, and requires a similar basic pay reduction for such assistance.