Last October Amtrak made an offer that several states have found irresistible: the publicly funded rail passenger corporation would beef up the states' service if its taxpayers would pick up 20 percent of the tab.

So far, seven states have taken advantage of the offer, opening up 19 new lines, and a half dozen more are applying for such services.

But Virginia, which itself applied for the funds for its Washington-Newport News corridor, has backed off because of the administration of Gov. John N. Dalton has an unwritten policy against paying the operating deficites of any mass transit operation.

Amtrak officials expressed surprise yesterday at the state's change of heart. "I'm disappointed," said Alexander Jordan, Amtrak's manager of state and local services. "This is an opportunity to grab ahold of something that is a winner. And the money that could have gone to Virginia may end up going somewhere else."

Businesses in the tourist-oriented corridor, hurt by the slump in highway travel, had been hoping the state would lood favorably on the Amtrak proposal. t

"We think [the additional service] would be a plus for the traveler -- very definitely -- and it would benefit us too," said Hugh DeSamper, director of travel and group marketing for Colonial Williamsburg, which last year fell under the 1-million mark in visitors partly because of the mid-summer gasoline shortage. "Any type of mass transit should be encouraged."

"We would really like to see this (train service)," agreed Vincent H. Ghaardo, manager of the Williamsburg Pottery complex, a retailing outlet that attracts 20,000 people on a peak weekend. "Everybody stands to benefit. The state will get its taxes."

"Obviously we're very much interested in any kind of mass-transit facilities that would make Virginia more convenient to tourists," said Marshall Murdaugh, director of the Richmond office of the Virginia Travel Service.

But the State-run Travel Service cannot afford to step on politcal toes, and Murdaugh said he is not about to urge those who appropriate the service's fund to spend more money on Amtrak.

Virginia Transportation Secretary George Walters is in nearly the same position. Although he says he strongly supports the increased train service he will not endorse any state expenditure that would run up against what he called the state's "unwritten policy" against assumption of any masstransit operating deficits.

Walters, whose agency filed for the Amtrak funds, said it would be up to the General Assembly or the state's localities to provide any funds for the Amtrak service. For the state to offer funds "flies in the face of state policy . . . (so) we are trying other methods of financing." he said.

Thus far, however, none of the tourist spots that stand to gain from the added train service has been willing to volunteer any funds for the trains, said Robert G. Corder, Virginia's rail administrator. He has been attempting to drum up support for the plan since it was first proposed in October 1979.

One proposal would have the affected localities and tourists spots pick up $313,000 of the projected $1.56 million first-year operating deficit, with Amtrak paying the remainder. No formula for sharing the costs among the localities has been devised and, some Northern Virginia localities, already burdened with Metro debts, are reluctant to subsidize a service that they see largely benefiting private enterprise and other localities in the state.

"We're having a lot of trouble coming up with money we need to solve the county's transportation problems," said Fairfax County Supervisor Nancy K. Falck (R-Dranesville).