Senate Finance Committee Chairman Russell B. Long (D-La.) said yesterday he expects the Senate to pass a tax cut this year, to be effective at the first of 1981.

"The sentiment on this committee and in the Senate is in favor of a tax cut this year," Long told Treasury Secretary G. William Miller as the committee opened hearings on a possible tax cut. The committee has been directed by the Senate Democratic majority to report a tax-cut bill to the floor by Sept. 3.

Miller reiterated the administration's opposition to action on a tax reduction before the election, but he dropped broad hints that President Carter might before the first of the year make a detailed proposal for cutting taxes.

As for the Sept. 3 reporting mandate, Miller declared, "Reporting a bill that could be a framework for discussion for action after the election would be a contribution."

Most of the Republican members of the committee continued to press for the proposals endorsed by their presidential nominee, Ronald Reagan, which include a 10 percent across-the-board reduction in personal income tax rates and a major increase in business depreciation allowances.

Even though most committee Democrats signed the resolution setting the Sept. 3 deadline, their remarks yesterday indicated considerable uncertainty. On the House side, where the Ways and Means Committee opened its own hearings Tuesday, there is distinct Democratic opposition to passing a tax cut this year.

Sen. Harry F. Byrd Jr. (Ind.-Va.), who did not sign the Senate resolution, did not declare himself for or against a tax cut but repeatedly took Miller to task for the sharply higher estimates of the 1980 and 1981 federal budget deficits announced last week by the administration. A tax cut would further increase the 1981 deficit, now put at about $30 billion.

Sen. Gaylord Nelson (D-Wis.) issued a statement cautioning against "any purely political, election-year, irresponsbile tax cut proposals which would simply fuel a new round of inflation." One of his legislative aides later said the senator "has not made a final decision" on whether a bill should be passed this year.

Sen. Lloyd Bentsen (D-Texas), who has been pushing for more than a year for a tax cut to spur business investment and increase productivity, said it "is important for the American people to know before the election whether the administration is committed to a tax cut" and, if so, what its scope would be. If that were the case, "I don't care whether the tax cut is passed before or after the election," Bentsen told Miller.

The administration has said it wants to postpone action to avoid a tax cut whose details were thrashed out in the "pressure-cooker atmosphere" of an election campaign.

In reply to a question from Sen. William V. Roth Jr. (R-Del.), one of the architects of the Republican tax-cut proposal, Miller said, "I think we are more in agreement than it seems...The issue is whether you do it before the election...The argument seems to be tied around election day, and that makes me nervous."

However, at another point in the hearing, the Treasury secretary indicated Bentsen's concern might be met before election day. "In the next few months, maybe the administration can be more specific" about its tax-cut intentions, Miller said.

Chairman Long, apparently somewhat uncomfortable with Miller's argument about enacting tax bills in an election-year atmosphere, recalled, "I've been around here 32 years, and I can't recall whenever it was any different." He relented a bit in a summary at the end of the hearing, however, telling Miller, "While your position at the moment is at variance with the prevailing sentiment in the U.S. Senate, there is a lot to be said for it."

Long, known for his subtleties in legislative maneuvering, is -- despite his statements -- raising doubts in the minds of some Capitol Hill tax experts about his actual intentions.

"Long is not all that enthusiastic about this tax-cut idea," said one, adding, "He may be 'slow-balling' the whole thing. Everything is moving according to the proper procedures, but it is moving very slowly. We could just run out of time."