Assuming the congressional results do not change, here's how the contingent election breaks down in the 103rd Congress:
For the House of Representatives (in which each state gets one vote):
Democratic-majority: 28 states (AL, CA, GA, HI, IL, IN, KY, LA, MA, MI, MN, MS, MO, MT, NJ, NY, ND, OH, OK, OR, PA, SD, TN, TX, UT, VA, WA, WV)
Republican-majority: 9 states (AK, CO, DE, FL, IA, NE, NM, WI, WY)
Tied delegations: 12 states (AZ, AR, CT, ID, KS, ME, MD, NV, NH, NC, RI, SC)
Independent: 1 state (VT)
Result: Bill Clinton is elected by the House on the first ballot with a vote of 29-9, with 12 abstaining.
For the Senate (in which each Senator gets one vote):
Democratic: 57 seats
Republican: 43 seats
Result: Al Gore is elected by the Senate with a vote of 57-43.
(This assumes that the Democrats are in the top two of the electoral vote count. If not, I suppose the Democrats vote in James Stockdale.)