President Carter and Senate Finance Committee Chairman Russell B. Long (D-La.) squared off yesterday over enactment of the tax-cut law before the Nov. 4 election, with Long hinting that he may join with Republicans and try and end-run to push the bill to passage.

In a televised news conference, the president said that with inflation still a major problem he is "standing firm" against a preelection tax cut. He said a "quick fix" would worsen the price spiral.

Howevr, Long, apparently frustrated in his efforts to force a prompt vote on tax reduction, yesterday said he will support a Republican attempt to add the bill to other tax-related proposals if the Senate leadership doesn't give in.

The Finance Committee has completed work on a $39.8 billion tax-cut bill meant to take effect in January 1981, but is running into opposition from Democratic leaders who are supporting Carter in the fray.

His announcement came after strong indications yesterday that Senate Majority Leader Robert C. Byrd (D-W.Va.) would not go along with a preelection vote on the tax-cut bill, even though the panel has stripped it of all troublesome narrow-interest amendments.

Although Byrd still has not made a final decision, several sources confirmed yesterday that he is leaning heavily against prompt action on the bill. Long and Byrd met yesterday in continuing talks on the issue.

Meanwhile, House Ways and Means Committee opposition to taking up a tax-cut bill this year appeared to soften somewhat yesterday as Rep. James R. Jones (D-Okla.) bolted from the majority and announced his support of a quick vote.

Only a day before, Ways and Means Chairman Al Ullman (D-Ore.) had announced that the committee's Democrats had solidly reaffirmed their opposition to consideration of any major tax-cut bill this year.

Carter, at his news conference yesterday, said he thinks the "recovery of the economic system is progressing very well," but stopped short of declaring the recession over. "We'll have our ups and downs," the president told reporters.

Asked about the the outlook for the economy, the president predicted that inflation will remain below double digits for the rest of this year, while the unemployment rate won't vary much from the present 7.6 percent.

Carter is opposed to any immediate congressional action on a tax-cut bill for fear that it would revive inflation psychology and send interest rates back up, possibly choking off recovery.

However, some Senate Democrats and Republicans following the lead of GOP presidential candidate Ronald Reagan, favor early action on tax cuts for individuals and business. The Finance Committee's bill came in response to their demands.

The GOP intention to tack the Finance Committee bill onto other tax related legislation was announced by Sen. Bob Dole (R-Kan.), ranking minority member of the panel.

He said yesterday that the most likely target would be a bill the Finance Committee approved yesterday to continue the existing user tax on airline tickets for another year.

He also listed related bills dealing with minor Social Security programs and renewal of general revenue-sharing. All three measures must be passed this session or the programs will expire.

Senate Republicans immediately ordered a "hold" on all Finance Committee legislation -- a procedural device designed to alert them whenever any of these measures is sent to the Senate floor.

Long said yesterday that he will continue his talks with Byrd to try to persuade him to allow the tax-cut bill to come to the floor. But he told Dole he would support the GOP move "if I had no other choice."

Byrd had said previously that he objected to quick action on the Finance Committee proposal, mainly because of fears that it might be turned into a "Christmas -tree" bill, laden with special-interest amendments.

The panel voted Tuesday, however, to forgo some 90 narrow-interested provisions it otherwise would have added to the bill, mainly in hopes of overcoming Byrd's apprehensions about the package.