The House and Senate are heading toward a shoot-out on the question of whether to refloat the Nimitz-class nuclear aircraft carrier President Carter sank last year.

On Thursday the House Appropriations Committee rejected arguments that the $2 billion carrier would be a sitting duck in the nuclear age, and approved a defense bill including the money to build it.

The rising price of oil was cited by Nimitz backers as a reason to opt for the nuclear-powered ship rather than the cheaper, oil-fired carrier that Carter prefers.

Last year, Carter felt so strongly against financing another giant Nimitz-class carrier that he vetoed the Pentagon money bill that authorized it. His veto was sustained.

But some backers of the nuclear carrier doubt Carter would go that far this year, citing the national mood for higher defense spending and the president's decline in public opinion polls.

The Senate Armed Services Committee took a compromise position on the carrier in passing its procurement bill. It voted money for an oil-fired Kennedy-class carrier, rejecting the administration request for an even smaller carrier.

Defense Secretary Harold Brown recently wrote the House that Carter would accept the larger Kennedy-class ship, but still was opposed to building another of the Nimitz class. The oil-fired ship is expected to cost $1.8 billion and the nuclear carrier, $2.36 billion.

The carrier issue will pit Sen. John Stennis (D-Miss.), who is chairman of both the Senate Armed Services Committee and the Senate defense appropriations subcommittee, against Chairman Melvin Price (D-Ill.) of the House Armed Services Committee as the two try to work out a compromise money bill.

The overwhelming votes in the House against settling for something less than the Nimitz-class carrier make it difficult for Price to budge, his aides say, in the upcoming House-Senate conference sessions.

Pentagon executives see the carrier issue as the biggest change in the congressional climate this year, not how much money will be appropriated for defense in fiscal 1980. They do not take seriously the Senate's action in raising budget ceilings to allow Pentagon budgets to rise by 5 percent in fiscal 1981 and 1982. That action is not binding, they point out.

"We're doing about as well as expected with money," said one Pentagon official, when asked for an assessment, "But not as well as last year."

In examining recent congressional actions on the pending 1980 budget, Pentagon officials conclude that they will get the full amount of the president's amended request from the Senate, but end up about $2.7 billion short in the House. They predict that House-Senate compromises on defense spending will leave them in good shape.

The House may vote next week on its $127.8 billion defense appropriations bill. The Senate defense appropriations subcommittee has not finished work on its bill, but is expected to be more generous than the House.

The Senate debated another major defense issue yesterday: Whether to resume draft registration. Sen. Sam Nunn (D-Ga.) made the case for this step in a Senate debate behind closed doors. But his bill requiring young men to register will not be brought up for a vote until next year, at the earliest.

Sen. Gary Hart (D-Colo.), a member of the Senate Armed Services Committee, argued that returning to registration and the draft would "merely prop up the current inefficiently structured land forces" by supplying the armed services with an unlimited number of soldiers.

He said Congress instead should address the question of whether it is time to tailor the nation's forces to geographic realities, perhaps emphasizing sea-based forces over land armies.

"If we adopt a maritime strategy," said Hart, "we need not return to the draft."