The Virginia House of Delegates bowed to 24 hours of intense lobbying and threats of political blackmail tonight and approved a compromise two-cent-per-gallon increase in the state's gasoline tax.

The latest development in a see-saw battle between Republican Gov. John N. Dalton and conservative, antitax legislators, virtually assures enactment of the tax boost. The tax increase measure now goes to the State Senate whose leadership long ago endorsed the proposal.

Passage of the measure also seems likely to remove uncertainty about the fate of a separate 4 percent sales tax bill passed by the House earlier. That tax would be added to gasoline sales in Northern Virginia to finance Metro transit operations there.

Together the two bills would increase the price of a gallon of gasoline in the Washington suburbs by seven cents a gallon in midsummer when the measure would go into effect.

The two-cent-a-gallon tax bill, which had been narrowly rejected last night, passed 54 to 43 tonight after supporters mustered 10 additional votes, six of them Northern Virginians who were convinced that powerful Senate Finance Chairman Edward E. Willey would kill the Metro-funding proposal if the Dalton bill failed.

The other four converts were Republicans summoned this morning to the governor's office for unusual one-on-one sessions with Party chief Dalton, who had placed his political prestige on the line with the bill.

The result was a no-holds-barred brand of politics lawmakers said they had seldom seen before in the capital of the Old Dominion where rough-house tactics usually are disdained.

"It's the worst pressure I've seen applied in many years," said Del. Richard Cranwell (D-Roanoke County). Cranwell led opponents of the tax increase, which would raise the state gasoline tax to 11 cents per gallon.

"My whole body's in a sling -- I'm really being squeezed on this," said freshman Republican Del. David G. Speck of Alexandria, one of the Northern Virginians who changed his vote today after meeting with Dalton. Speck said he switched "because I was persuaded a negative vote could jeopardize the Metro tax in the Senate."

Another Northern Virginian, David G. Brickley, said he and fellow Prince William County Del. Floyd C. Bagley switched their votes after a mid-afternoon conference with Willey, a longtime Metro foe and conservative ally of Dalton.

"He said he'd do everything in his power to kill the Metro bill," said Brickley. "He made no ifs, ands or buts about it. I don't like it, but it's a political reality."

Last night's 49-to-44 vote to kill the tax proposal had stunned Dalton's supporters, who thought they had lined up enough votes to pass the bill. A sizable portion of the opposition came from Northern Virginia, where 15 to 19 delegates had opposed the bill because they had already voted for the campanion measure tacking a four percent regional gasoline sales tax on area motorists to pay for Metro.

House Republicans, many for whom Dalton campaigned for vigorously last fall, also had opposed the bill yesterday by a 17-to-8 margin.

"The governor was very upset," said Dalton spokesman Paul G. Edwards. "I've never seen him more deeply affected in the time I've been with him. He's normally not the kind of governor who cracks the whip . . . but this is a question of the relationship between the governor and his own party."

For Republicans, the hard-sell began early this morning when Dalton called a half-dozen legislators to the Governor's Mansion for breakfast and a pep talk. It continued during the day with individual sessions.

"He told me, 'I campaigned for you and I've only asked you to do one thing since you've been down here," said James H. Dillard, a Fairfax Republican who refused to cave in.

"He was trying to twist our arms out of the sockets," said Del. Robert E. Harris, another Fairfax Republican who said, "I told him no. I tried to explain why but he didn't want to hear it. It was straight hardball -- just plain pressure."

Northern Virginia Democrats found themselves under equal pressure from the legislative leadership. In private meetings, Speaker A. L. Philpott, a supporter of the increase, warned the Northern Virginians they were endangering the Metro bill by fighting the statewide tax.

"It took a lot of arm-twisting and cajoling to get the Metro bill out of this floor," said Philpott. "After all of us agreed to vote for them (the Northern Virginians), they turned around and voted against us and they can expect the same treatment if the Metro bill comes back here."

Willey denied Brickley's statement that he too had pledged to sabotage the Metro bill, which presently is before his Senate Finance Committee. But other area lawmakers said they also had been told by other committee members that the Metro bill was being held hostage for Dalton's proposed statewide tax.

"The message from the Finance Committee this morning was loud and clear," said Del. Vincent F. Callahan (R-Fairfax).

By lunchtime, the proposal's supporters thought they had lined up the 51 votes necessary to move for reconsideration and passage of the bill. They were uncertain and put off the final confrontation until tonight's session.

One problem was that while proponents were gaining converts among Republicans, their support among Democrats was hemorrhaging. House Majority Leader Thomas W. Moss and two fellow Norfolk Democrats who had voted for the bill yesterday opposed it today.

"I told the governor I'd gone as far as I could go on this thing," said Moss, who blamed lack of credible statistics from the state highway department for the Assembly's reluctance to approve the tax. "It's hard enough to vote for a tax increase when the numbers are clear."

Opponents made a last-ditch effort this evening to stem the tide and defeat the bill. Cranwell argued what was at stake was "the credibility of this House over the credibility of the administration" and said lawmakers would be hard-pressed to tell voters "why one day later we can reverse our decision on an issue of this magnitude without any new evidence."

Del. Clinton Miller (R-Shenandoah), angered by the arm-twisting done by fellow Republican Dalton, said, "I don't like it (the tax) and I'm not going to vote for it."

Miller, added, "I'm not going to bend, I'm not going to break. The people of Virginia are going to remember . . . I don't think the Republican Party stands (for) that type of imposition of a tax."

Proponents said tonight's passage sets the stage for a quick passage of some form of the Metro tax bill. Many lawmakers expect a move to cut the Metro measure down to 2 percent to lessen its impact on motorists.

"What a difference a day makes" said Edward after today's vote. He said Dalton "was very pleased by the outcome but he's unwilling to predict what will happen in the Senate."