President Carter prodded Congress yesterday to do more than just split the differnce between its two versions of his proposed oil tax. And Sen. Edward M. Kennedy (D-Mass.) said Carter should be threatening to use the veto power to get the strongest possible tax out of a House-Senate conference.

The House, meanwhile -- as conferees prepared to meet today to begin reconciling their differences -- caved in early and enthusiastically to a Senate demand for a tax break for people who sell inherited property.

By a vote of 326 to 77, the House instructed its conferees to go along with a Senate rider on the oil bill repealing a 1976 tax "reform" raising capital gains taxes on the proceeds from the sale of inherited wealth.

Under the 1976 "carry-over basis" rule, an heir would pay taxes on the increase in value of property from the time the deceased bought it to the time the heir sold it. Previously taxes were owned only on the increase in value from the time the heir acquired the property until it was sold.

The change was so controversial that its effective date was postponed until 1980.

The Senate rider would simply take it off the books when the oil tax passes.

Exactly when that will be was unclear yesterday. House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said he would be "greatly surprised" if the tax bill could be wrapped up before Congress leaves on its Christmas recess.

And Senate Majority Leader Robert C. Byrd (D-W. Va.) said, "It would make a nice Christmas present, but that doesn't mean Santa Claus will bring it down the chimney."

Quoting Carter's remarks at a breakfast meeting with congressional leaders, O'Neill told reporters that the president wants more than a 50-50 split between the Senate and House versions of the tax -- meaning more than $228 billion in revenue over the next decade.

The Senate bill, as approved Monday night, would raise an estimated $178 billion by 1990. The previously approved House bill would raise $277 billion over the same period, close to what Carter first asked.

"What he [Carter] thinks equitable is better than 50 percent of the difference," said O'Neill. He added that Carter, although he had wanted a bill by the end of this year, would rather wait than see a weak bill adopted under pressure of a vacation deadline.

Carter did not say what would be enough to avoid a veto and possible reimposition of controls on crude oil prices. Nor did he explicitly threaten a veto.

In a statement issued earlier, Kennedy, Carter's principal challenger for the Democratic presidential nomination, criticized Carter for not threatening to veto a weak bill.

"Those of us who have sought to strengthen the Senate bill have had to proceed without the most basic leverage usually afforded proponents of a presidential initiative -- the threat of a veto," said Kennedy.

Carter and Kennedy apparently do not disagree, however, on how large the tax should be. Both contend it should be closer to the House version than the Senate's.

The tax would be levied against the huge proceeds that oil producers are expected to reap from Carter's decision to phase out crude oil price controls. eThe House bill would take about 60 percent of the producers' net profits, while the Senate bill would take about 40 percent.

Meanwhile, the proposed tax also came under fire from a different direction, with the American Petroleum Institute charging that it would increase the nation's dependence on foreign oil and encourage oil cartel price increases. "It is, pure and simple, a revenue-raising measure at the expense of the American consumer," said Charles J. DiBona, president of the API, which represents oil producers.