The Senate Finance Committee ran into difficulty yesterday in a move to force a prompt floor vote on its $39.8 billion tax-cut bill, as other key Democrats voiced opposition to taking the bill up before the election.

At a luncheon meeting of key Senate leaders, Democrats not on the Finance panel reportedly argued strongly against any pre-election action on the bill, contending that inflation-concious voters don't want taxes cut right now. b

Sources said among those opposing a pre-election floor vote was Sen. Ernest F. Hollings (D-S.C.), chairman of the Senate Budget panel, who reportedly warned the cut would enlarge the budget deficit.

At the same time, the White House yesterday intensified its lobbying in an effort to ward off a pre-election vote. President Carter opposes enactment of a tax cut this year on grounds that it might rekindle inflation psychology.

Senate Majority Leader Robert C. Byrd (D-W.Va.), who previously has opposed taking up the tax bill before the election, put off any decision on the issue for several more days. Byrd served as chairman of yesterday's meeting.

The opposition in the Democratic caucus yesterday marked an unexpected setback for Finance Committee leaders, who had hoped to win prompt approval from Byrd to take up the tax-cut bill on the floor next week.

Primarily to meet the majority leader's apprehensions about a pre-election floor vote on the measure, the Finance panel voted Tuesday to scrap some 100 pending narrow-interest amendments and approve a "clean" bill.

The decision to reject the panel's traditional end-of-the-year tax-break package had constituted a major departure from its previous practice. The committee has made a reputation for approving special-interest bills.

Both Byrd and top Carter administration officials had expressed fears that a tax bill considered before the election might be turned too easily into a "Christmas-tree" bill, laden with undesirable narrow-interest tax breaks.

However, Finance Committee Chairman Russell B. Long (D-La.), in concert with the panel's Republicans, pushed through unanimous agreement to forego the special-interest proposals to overcome Byrd's objections.

The Finance panel members also vowed to act as a group to oppose any narrow-interest amendments that other seantors might bring up when the tax bill comes to the floor. The Finance Committee has 20 members.

Yesterday's opposition reflected a cooling of the tax-cut fever that hit the upper chamber a few months ago, when Senate Democrats -- panicky over GOP candidate Ronald Reagan's tax-cut plan -- bolted and vowed one of their own.

Sources said yesterday many Democratic senators who surveyed their constitutents during the Labor Day recess found voters decidedly lukewarm about a tax cut this year, with many of them fearful it would exacerbate inflation.

Several nationwide polls in recent months have shown a large proportion of Americans suspicious of a tax reduction, asserting it probably would not grant them much individual relief and would only widen the budget deficit.