Veterans Educational Opportunities Enhancement Act of 2001

Veterans Educational Opportunities Enhancement Act of 2001 - Amends Federal veterans' benefits provisions to allow the basic pay reduction for entitlement to veterans educational assistance under the Montgomery GI Bill to be taken over two years (currently one year).

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.