The governors of Virginia and Maryland visited key members of the Senate's public works committee yesterday in a bid to win support for an additional $600 million federal payment toward a new Woodrow Wilson Bridge.

Virginia's James S. Gilmore III (R) and Maryland's Parris N. Glendening (D) made the unheralded trip to Capitol Hill, where the funding package proposed by the Clinton administration is encountering slow going in Congress and concern is rising about the future of the region's premier crossing.

After the hour-long, closed-door session in the office of Sen. George V. Voinovich (R-Ohio), chairman of the transportation subcommittee, Gilmore said the two states may not prevail in wresting a funding commitment from Congress before its anticipated recess next week. "We still have a distance to go," Gilmore said. "We can't predict if it's doable or not. . . . It may have to go to a future Congress before it'll be worked out."

Slowing the efforts to gain congressional approval this year was the death last week of Sen. John H. Chafee (R-R.I.), chairman of the Senate Environment and Public Works Committee. Yesterday's meeting was a chance for the governors to press their case not only with Voinovich but also with Robert C. Smith (R-N.H.), the new chairman of the public works committee, and Max Baucus (Mont.), the ranking Democrat.

The governors reminded their hosts that the Wilson Bridge is a crucial link for private and commercial traffic along the East Coast and that their states have each pledged to pick up $200 million of the $1.9 billion tab for replacing the rapidly deteriorating span.

But some members of Congress, most notably the influential chairman of the House transportation committee, Rep. Bud Shuster (R-Pa.), have said the federal government has already promised its fair share--$900 million approved last year--and they are reluctant to provide more. A spokesman for Shuster's committee said it has taken no action since a hearing on the proposal early last month, offering little hope that the $600 million shortfall will be closed soon.

"You don't start the project unless there's full funding," Glendening said after the session yesterday. "We have a problem here."

Under an administration plan announced in June after about a year of negotiations with the states, the federal government would boost its contribution by spending $150 million a year for four years beginning in 2004.

Sens. Charles S. Robb (D) and John W. Warner (R), both of Virginia, have been trying to shepherd the proposal through the Senate and attach it to a broader spending bill that could be approved in the waning hours of Congress. Both issued statements yesterday saying they are still exploring avenues for obtaining the money.