President Carter suffered two more serious setbacks to his energy program yesterday as the Senate Finance Committee tentatively voted to kill his wellhead tax on oil and the Senate cast another vote against his plan to continue price controls on natural gas.

The Senate did vote 77 to 17 to invoke cloture and limit debate on the natural gas issue. But more than 500 amendments have been introduced and can be forced to a vote even though speaking on the issue is now limited to one hour per senator. A group of senators opposed to increasing the price of natural gas promised to filibuster for weeks by forcing dozens of roll-call votes.

As Senate leaders worked to resolve the natural gas pricing question. Carter went before television cameras to denounce the gas industry's campaign for removing price controls, saying deregulation would cost consumers $10 billion a year. He urged the Senate to vote for the public interest over special interest. The House approved the President's plan to continue price controls at a higher level. Over the weekend, Carter came close to threatening to veto an energy bill that provided for deregulation of natural gas.

The Senate Finance Committee voted 11 to 6 to kill the crude oil tax, but efforts will be made today to revive it.

The tax, which the administration calls the centerpiece of its energy conservation plan would nearly double the cost of domestic crude oil by taxing it up to the world price in three annual steps. Carter wants to rebate the $14 billion a year that the fully effective tax would produce to the public to avoid an adverse impact on the economy.

But a strange coalition of consumer groups and the oil industry has formed to try to kill the tax for different reasons. Last week the Finance Committee told the administration that its oil tax was dead unless the money was put to work producing more energy, meaning it would go to producers.

Yesterday morning, Assistant Secretary of the Treasury Laurence Woodworth, former chief tax adviser to the committee, appeared before the panel to make a new proposal.

Woodworth asked that the tax be rebated to the public the first year and that about half be rebated to low-income people in future years. Under this plan, the rest could be used to produce more energy.

The administration also proposed a new incentive for the oil industry to pump hard-to-reach oil from abandoned wells. Woodworth proposed a 1 per cent decline rate, meaning that each month 1 per cent of the nation's "old" oil, which has a price ceiling of $5.50 per barel, would be switched to the "new" oil category, which has a ceiling of $11.50. This would mean a $6-per-barrel increase to the producer, but it would not be paid to him until Oct. 1, 1981. This is something like the so-called "ploback," or rebate, of part of the tax to producers which the administration denounced and defeated in the House.

Finance Committee Chairman Russell B. Long (D-La.) asked the committee how it felt about the principle of the decline rate. Members favored it 13 to 3. Long said he would prefer a 1 1/2 per cent rate and would like to see the higher price paid to oil producers starting 2 1/2 years sooner, in May, 1979.

Then, without further discussion, Sen. William V. Roth Jr. (R-Del.) prevailed, 11 to 6, on his motion to strike the oil tax from the bill. Roth had arued last week that the economy needs a tax cut not a tax increase. Six Democrats, including Long opposed the motion to kill the tax.

Long warned that "we'll have to put in back or there'll be no bill."

After the meeting, Woodworth called the oil tax "crucial" to the President's energy package and added: "I don't think this will be the final action of the committee."

Usually when the Senate musters the necessary 60 votes to limit debate on an issue, the opposition has a clear majority for it. But it is not yet clear that any of the many natural gas pricing proposals, has such a majority. However, each vote makes it appear that the lan to deregulate newly discovered onshore gas - being pushed by Sens. James B. Pearson (R-Kan.) and Lloyd M. Bentsen (D-Tex.) is ahead.

Carter would raise the ceiling price on newly discovered gas from $1.45 per thousand cubic feet (mef) to $1.75 and extend controls to cover gas consumed in the state where produced as well as that piped across state lines.Unregulated intrastate gas is now selling at a little less that $2 per mef. The Pearson Bentsen plan would permit new gas to sell at what the market would bear, but would continue old gas under controls.

At the White House yesterday, the President resorted to his favorite weapon - televisin - on an attempt to salvage his gas pricing plan.

Employing familiar language, the President read a prepared statement characterizing the Senate showdown over deregulation as a struggle between "the special interests" and the American people.

"It is time for the public interest to prevail over the special-interest lobbyists," he said.

Carter appealed to the Senate to "act responssibly in the interest of the great majority of Americans and to reject the narrow special-interest attacks on all segments of the energy plan." He said "the special interests must not be allowed to jeopardize our energy future."

Sen. Howard M. Mezenbaum (D-Ohio), a leader of the group fighting higher gas prices, said the filibuster traditionally has been used by groups trying to defeat civil rights, consumer or labor legislation.

"What is, so terrible about using it in behalf of consumers?" he asked.

Most senators apparently thought in was being abused as when Sen. James Abourezk (D-S. D.) demanded Friday that an amendment offered by Sen. George McGovern (D-S.D.) be divided into its 20 component parts and forced to 20 roll-call votes.

Among Maryland and Virginia senators, only Paul S. Sarbanes (D-Md.) voted against cloture.

After the vote, Majority Leader Robert C. Byrd (D W.Va.) said the Senate has "indicated very clearly that it wants to vote." But also warned that there were hundreds of amendments pending and cautioned senators to say close to the Capitol for the next few days because there will be "many votes."

The Senator debated natural gas all last week Byrd said that if the issue isn't disposed of by the weekend there will be another Saturday session. And there was talk of all-night sessions of the kind that were used to break civil rights filibusters, a tactic that hasn't been used in recent years.

One of the first things the Senate did after voting cloture was to vote, 53 to 39, without debate to table a proposal by Sen. Edward M. Kennedy (D-Mass.) that was essentially Carter's natural gas provision. But because of the parlamentary situation, the Kennedy proposal could not be amended. There will be other chances to vote on the President's plan.

But the two votes on the issue thus far cannot give Carter much comfort. Last Thursday the Senate voted, 32 to 46, not to table Pearson-Bentsen and thus to keep that anti-Carter proposition alive.

Sen. Henry M. Jackson ;D-Wash.), floor manager of the gas bill, floated a compromise last weekend that would increase the ceiling to $2.03 per mef. But he said yesterday that plan was gettin shot at from both sides and appeared to be a loser.