Tax-cut fever appears to be abating slightly in the 96th Congress.

After an initial flush by Senate Democrats in June, prospects for enactment of a tax bill this year have steadily dimmed, and many observers now are skeptical any legislation will be passed even in a lame-duck session.

"If I had to be now, I'd bet there'll be no bill before sometime in 1981," said one key insider close to the current proceedings. "I just don't think there's enough support, either here or out on the hustings, he added.

The somewhat dampened mood contrasts sharply with the outlook in June, when Senate Democrats -- panicked by a new tax-cut plan proposed by Republican president candidate Ronald Reagan -- pledged a tax bill of their own by Sept. 3.

Since then, however, then have been several new developments -- all of which have tended to slow the rush for a tax cut before the election:

The Carter administration, which had hedged earlier when the Senate Democrats began their panic run, came out strongly opposed to prompt tax-cut legislation in congressional testimony in mid-July.

House Ways and Means Committee members, returning from a July 4 recess and talks with their constituents, confirmed that many voters are suspicious of a tax cut and not eager to see one enacted promptly.

Although the panel plans to continue holding hearings on the issue, committee leaders say they have no plans to schedule actual bill-drafting sessions unless forced into action by the Senate Finance Committee.

Finance Committee Chairman Russell B. Long (D-La.) is pushing actively for a tax bill this year, but -- because of his own re-election campaign -- isn't expected to have time to draft one before his Sept. 13 primary.

While the finance panel has slated a markup session for the week of Aug. 18, insiders say Long may not show up for all the sessions, and both Democrats and Republicans are splintered over what ought to go into any new bill.

Even the push for faster business depreciation writeoffs -- possibly the most broadly supported tax-cut idea now being floated hasn't settled on a single proposal. And Republicans aren't Fully united on the Kemp-Roth-Reagan plan.

Although Long suggested in a July 25 speech that the tax bill might be considered in a special session after the November election, some sources say this, too, is becoming less likely as the weeks go on.

For one thing, onlookers say no matter which presidential candidate wins, it's unlikely there'll be much pressure from the White House for action on a tax-cut package anytime this year.

If Reagan is elected, these observers reason, he won't want the lawmakers to move until he actually is in office. If Carter is victorious, he won't seek a rush enactment. And Republicans would be reluctant to go along with any bill.

There's also the question of whether Congress will want to schedule action on a tax bill during a lame-duck session. The lawmakers already are going to have to act on the budget resolution. Many think that will be headache enough.

Finally, even the Senate Democrats have not pushed ahead with very much vigor. A special task force meeting last night approved a few general economic pronouncements, but did not get into any recommendations on a possible tax cut.

To many key observers, the best indication may come Aug. 18, at the Finance Committee's initial mark-indication may come Aug. 18, at the Finance Committee's initial mark-up session. It Long and the Republicans have a viable plan, there still could be a bill this year. If not, it'll be 1981.

The feeling on Capitol Hill is that while the tax cut isn't yet dead, it's not quite as lively and kicking as it seemed a few weeks ago. But the betting is still up in the air.