Senate Majority Leader Robert C. Byrd yesterday said he has given up hopes for passage of President Carter's energy package this year.

However, the West Virginia Democrat said he remains confident that their differences on the package before Christmas and that the measure will be passed sometime early next year.

Byrd refused to speculate exactly when that might be. But he made it clear he intends for the Senate to be in recess from the week before Christmas until Jan. 19. "I don't think deadlines are important," he told his weekly news conference on Capitol Hill. "What is important is that we get an energy bill."

Carter and congressional Democratic leaders have put their joint prestige on the line over the fate of the energy package, repeatedly saying that it would largely determine the success or failure of the President's first year in office.

Conferees, however, have moved at a turtle's pace in resolving differences between House and Senate-passed versions, and are still tied up on the explosive issue of natural gas pricing.

Byrd tried to divert attention from the delays over the bill - which he had previously said would be passed before Congress adjourned for the year - by lavishly praising Carter and Congress yesterday.

"The measurement of this Congress will be what it does on energy," he said. But "even without it. I'm willing to declare a victory and go home."

Byrd said he has "a very good personal relationship" with Carter, adding that any Saturday he wants to see the President "I just call up and I stop by."

"He wears his blue jeans and I go down in whatever I'm wearing," he said.

On other matters, the Majority Leader said:

He and Minority Leader Howard H. Baker Jr. (R-Tenn.) have lost their original enthusiasm over televising floor debate on the Panama Canal treaties.

There is a "general agreement" in the Carter administration that any tax cut next year should not be tied to any broad tax reform measure.

He adamantly opposes any deal to obtain testimony from Tongsun Park, the central figure in the alleged Korean influence-buying on Capitol Hill, if it forcloses Park's cooperating with congressional committees probing the matter.