The Senate signaled yesterday that it may stiffen its proposed windfall profits tax on major oil companies, just a day after virtually exempting smaller independent producers from the legislation.

But opponents blocked immediate action on the measure amid suggestons that a filibuster threat hanging over the Senate might materialize on this issue. Sen Bob Dole (R.Kan.), who at one point said it might take "several days" to talk about the issue, said last night that opponents would caucus today on strategy and suggested a compromise was possible. Majority Leader Robert C. Byrd (D-W. Va.) said he expected the issue to be resolved today.

The Senate's signal yesterday came on a 39-to-58 vote against derailing an administration-backed amendment to strengthen the tax by increasing from 60 to 75 percent the proposed rate on oil from wells discovered between 1973 an 1978, which amount to more than one-third of domestic production.

This would add an estimated $22.5 billion to the original anticipated yield from the tax over the next decade, more than wiping out the $10 billion lost from exempting the independent producers. The Senate bill originally was expected to take in $138 billion by 1990, only half as much as the president proposed and the House voted.

Yesterday's vote preserving the tax increase proposal indicated -- but did not guarantee -- that the Carter administration will be able to chalk up its first real victory in a thus far unsuccessful effort to strengthen the Senate bill.

In its biggest defeat on the tax bill, the administration tried in vain earlier this week to persuade the Senate to adopt the House version and thereby double the anticipted yield.

The Senate's refusal to go along with the House bill prompted Energy Committee Chairman Henry M. Jackson (D.Wash.) to call on President Carter yesterday to reimose price controls on oil. Jackson, a persistent critic of Carter's acton last spring to lift crude oil price controls gradually before they are due to expire in 1981, said the Senate has made a "charade" and a "whitewash" out of Carter's plan to retrieve some of the proceeds for the taxpayer.

Accusing Carter of erring by lifting controls before Congress has passed a strong windfall profits tax, Jackson said, "I can see no reason to continue the whitewash . . . anything short of price control reimposition will cheat the American people for the benefit of the oil industry."

Sen. Edward M. Kennedy (D-Mass.) has taken a similar position, attempting to make decontrol a major issue in his presidential campaign, although he and Carer agree basically on the desirability of strengthening the tax.

Taken together, this week's votes to exempt the first 1,000 barrels a day of oil drilled by independent producers while preparing to deepen the tax bite on the major integrated oil companies gave senators the best of two political worlds: giving the "little guys" incentives to go out and drill more while socking it to the big oil companies (although some of the small producers are in fact pretty big).

Yesterday's vote represented a setback to Senate Finance Committee Chairman Russell B. Long (D-La.), who contended that a 75 percent levy on oil discovered after 1973 would be "confiscatory" and a drag on domestic production. Longs committee had applied the 75 percent rate to oil discovered before 1973 but reduced it to 60 percent on newer oil as a presumed production incentive.

Long has been trying to fend off strengthening amendments with the agrument that the committee bill is a carefully crafted compromise designed to encourage production as well as retrieve some of the decontrol windfall.

However, in yesterday's brief debate before Long moved unsuccessfully to table the tax increase proposal being sponsored by Sens. Bill Bradley (D- N.J.) and John H. Chafee (R-R.I.), Chafee cited a Congressional Budget Office assessment that it would have little if any effect on production.