The Senate set up a head-to-head confrontation with President Carter yesterday by passing a weakened version of the waterway user charge bill - a version that Carter has explicitly pledged to veto.

Despite a day-long lobbying blitz by a large team of administration aides - and personal telephone calls from the president to Democratic senators - the Senate defeated, by 43 to 47, the waterway bill sponsored by Sen. Pete Domenici (R-N. M.), which Carter had endorsed.

Thereafter, the senators easily approved an alternative offered by Russell B. Long (D-La.). In a letter to the Senate Monday, the Carter administration said the president "will not sign" the Long bill.

Since the House has already passed a waterway toll bill, yesterday's Senate action means that some form of waterway fee will win final congressional approval this year. That marks a fundamental change in federal waterway policy; the government has never imposed any fee on the barge lines which use the multibillion-dollar system of inland waterways built and maintained with federal funds.

But what will happen after the bill leaves Congress is not clear. Transportation Secretary Brock Adams said after yesterday's vote that "this means the bill will be vetoed." But Long predicted the president was likely to sign the measure despite the veto threat. "I don't think he's as adamant as that letter makes him sound," Long said with a gentle grin.

The bill the Senate approved would impose a federal tax on the diesel fuel used by barges on the inland waterways. The tax would go into effect, at a rate of 4 cents per gallon, when construction starts on Lock and Dam 26, a major barge facility on the Mississippi at Alton, Ill.

It would increase to 12 cents per gallon eight years later.

The Senate's 12-cent-per-gallon tax would be twice as high as the waterway fee that the House passed last year. But it is smaller than the fee Domenici and the administration had been pushing.

The Domenici bill would have established, in addition to the diesel fuel tax, a separate set of charges linked to the government's annual expenditure for waterway construction. By forcing the barge lines to pay part of the government's construction costs, Domenici argued, the Senate would make the bargemen think twice before lobbying for expensive new water projects.

In the administration's letter Monday, Adams told the Senate that the administration, too, backed this "cost recovery" concept, and that Carter would veto the bill if it were not included.

If Carter carries out that threat, he would irritate a considerable segment of Congress.

The waterway bill includes more than the user charge provision and the authorization for the Alton barge facility. It also contains about $2 billion in "pork barrel" projects for 34 different states. These are projects that incumbent members of Congress love to boast about on the campaign trail.

Long and his allies were telling senators before yesterday's vote that Carter would probably back down and sign the bill even without the "capital recovery" addition to the waterway fee. Several members said last night that they agreed.

"The senators just did not believe that the president would go to the mat on this bill," said Sen. John Danforth (R-Mo.), who worked with Long to defeat the administration-backed proposal. "We have given him a substantial waterway charge, and most of us don't think the president will really insist on more."

Domenici had been fairly sure of victory ever since he heard last week that the administration would back him with an explicit veto threat.

But by noon yesterday he realized that his version of the bill was in trouble.

It was simply a matter of clout. Long, the chairman of the Senate Finance Committee, had recruited Sen. John Stennis, (D-Miss.), the Armed Services Committee chairman, and Sen. James Eastland (D-Miss.) to lobby their committee members in support of the weaker version of the bill.

It was too much firepower for Domenici, a first-term Republican whose senior committe eslot is ranking minority member of the Subcommittee on the Outer Atmosphere, to overcome.

The Senate's five-hour floor debate on the waterway bill was desultory, but the atmosphere was electric in the reception room just off the floor, where barge industry lobbyists kept colliding with their adversaries from the administration in their efforts to buttonhole senators for one last attempt at persuasion.

The floor was a sea of confusion during the evote. Several senators seemed uncertain about what was happening. Sen. John Heinz (R-Pa.), a Long supporter, voted for Domenicis version by mistake, but Danforth rushed over and led Heinz by the elbow back to the etally sheet to get the Pennsylvania's vote in the right col-Pennsylvania's vote in the right column.