The congressional politics surrounding President Carter's five-part energy legislation is beginning to resemble a family squabble at the dinner table.

"The House leadership, playing stern papa, is telling the Senate: no dessert until you eat your spinach.

The spinach, in this instance, is the compromise version of natural gas deregulation, supported by the Carter administration and a fragile majority of House-Senate conferees, but still vulnerable to filibuster and attack.

Fifteen Democratic senators called on Majority Leader Robert C. Byrd (D-W.Va) and Energy Committee Chairman Henry M. Jackson (D-Wash.) yesterday, urging them to pry loose one or maybe two other parts of the energy package and let the Senate vote on them first, before there is another nasty showdown on natural gas.

Sen. James Abourezk (D.S.D.), who staged a one-day parliamentary slowdown in the Senate Monday and threatens another filibuster if the matural-gas compromise is called up for Senate approval next week, said House leaders are "rat-holding" two other measures - on utility rate revision and conservation - which could be enacted without controversy.

House leaders, naturally, deny all this. At the same time, they think the Senate should vote on, the natural-gas bill first, the easy ones later, and have arranged the drafting of conference reports accordingly.

"There are dessert items, not the main entree," said Rep. John D. Dingell (D-Mich.), a leader among the House conferees.

"We are only trying to be helpful, not to dictate," Dingell said, with droll disregard for Senate egos. "We know the Senate wants to pass natural gas and we are anxious to help them. It's called cooperation."

These back-and-forth barbs would be mere parliamentary fluff except the stakes are so enormous. The natural-gas compromise bill would mean anywhere from $13.6 billion to $28 billion in increased revenue for the gas industry by 1985. More immediately, its passage would be an important political victory for the president.

For many senators and representatives, the politics looks a bit different and goes like this: they would like to go home to fall compaigns and proclaim that, by golly, they did something about the "energy crisis" - even if that only means supporting the weaker and least controversial measures, considerably watered down from Carter's original proposals.

If the Senate gets tied up first in a nasty fight over natural gas, that will postpone and perhaps greatly complicate the speechmaking. On the other hand, from the administration's view-point, if the Congress enacts the easy ones first, they might just refuse to swallow the hard ones.

Abourezk and Sen. Howard M. Metzenbaum, (D-Ohio), leading liberal opponents of the gas bill, figure they may pick up some allies if senators vote first on the other measures.

Senators are reluctant, Metzenbaum explained, "to vote against amorphous thing called the national enery plan. Once they've had an opportunity to vote for one or two other pieces, they can vote their conscience on natural gas."

Yesterday's meeting was inconclusive, but Jackson offered a vague promise to inquire if one other measure might be available for Senate passage first.

As it stands, the natural-gas provisions are to be made public tomorrow night and, at the least, the next week or 40 days should produce a lot of high-stakes pushing and shoving.

But the Democratic leadership does not hold all the cards. Senate conferees still have the ability to spill the whole plate of spinach, if they don't like it.

Under pressure from them, orchestrated in the main by Sen. Clifford 2. Hansen (R-Wyo.), Jackson agreed earlier to public circulation of the compromise language for 72 hours before it is submitted to the Senate for a final vote - and the Abourezk filbuster.

"The idea," Hansen, explains "is that most of us recognize it is a very complicated piece of legislation . . . This gives our constituents a chance to look at it before it is voted on."

Hansen said he thinks that such a situation, with industry, consumers and antidergulation forces howling on the sidelines over objectionable commas and curious language, could seriously threaten the compromise bill.

"Yes, there is a real possibility that it would fall apart," Hansen said. "In a bill of this complexity, in which so many promises have been made, it will be difficult for them to deliver everything that's been promised."

For its part, the House leadership has insisted all along that the Senate must act on natural gas and all the other measures before the House will take up any part of the energy package.

Making the point, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) last week ordered the Senate approved coal-conversion portion of the package held at his desk, thus preventing a final House vote on the bill.

Senate adoption of the coal-conversion portion - ahead of natural gas - also were rooted in this same complex political skein. The idea had been to pass it while President Carter was at the economic summit in Bonn two weeks ago, which would have been a feather of sorts in his negotiating bonnet.