GOP wants economic plan -- and fast

President Reagan is given until next fall by party strategists to convince Americans his economic program can succeed.

His political test for 1983: how to pull the United States economy out of recession and rev it up quickly enough so that next year's recovery will not still feel like hard times.

Treasury Secretary Donald T. Regan proposes moving up the third year of scheduled tax cuts from next July to Jan. 1, ''to get this economy moving faster ,'' he explains. Transportation Secretary Drew Lewis has proposed raising the gas tax some 5 cents a gallon to finance a jobs program.

But the proposals fall short of the concerted White House offensive some Reagan supporters say they would like to see. The proposals are viewed as possibly useful, yet essentially piecemeal, tinkering. The proposals reflect a divided White House - part still wedded to the Reagan's fundamental principle that government spending is the problem, and a moderate and pragmatic White House congressional Republican wing that would prefer more active use of government leverage to stimulate the economy.

Internal White House feuding is seen as an inducement for Republicans on Capitol Hill to wander from the Reagan camp. The administration has been slow to seize the political initiative after the election, some Republicans complain.

The Democrats bear their own handicap in the economic growth game. ''We don't have a quarterback,'' observes one Capitol Hill Democrat. The Democratic leadership struggle will itself be in full swing next year, with as many as seven presidential nomination campaigns underway, dividing the Democratic focus.

Still, the growth issue is more directly Reagan's, since he is the incumbent who primarily shaped the programs in place.

''The administration has maybe a year, but no more than that, to perform on the economy,'' says one GOP strategist. ''People have got to have the strong feeling, by the time we get to the end of next year, that there's no more worry about the economy - it may not be perfect yet, but it's going to be, quickly. And unless you have them in that frame of mind, you're in bad shape.

Impatient challenges to Reagan's current course are already emerging on both sides of the GOP spectrum.

''Two percent growth is unacceptable to the American people,'' says Rep. Jack Kemp (R) of New York, a conservative spokesman. On the moderate side of the Republican aisle, Sens. Howard H. Baker Jr. of Tennessee, Pete V. Domenici of New Mexico, and Bob Dole of Kansas are restlessly pushing their own prescriptions for action - with their own White House or Senate reelection ambitions as a backdrop.

Economists have been lowering their forecasts for next year's growth in the economy, from the 3 percent range down to 2 or 2 1/2 percent. Next year ''will be slow,'' says Sarah Johnson, an economist with Data Resources Inc. ''Business investment will continue to decline. That, combined with a strong dollar, which weakens exports, will certainly be a drag on the economy.''

But many economists and lawmakers view the tax cut move-up warily. Rudolf Penner, American Enterprise Institute tax and budget analyst, says the economy may have had enough stimulus already. Actions like the eased federal reserve monetary policy since summer, and last July's tax cut, can require a six months or so to show effect. Mr. Penner says he would wait until the Christmas buying mood is registered this December.

''It all revolves around the consumer,'' Penner says. The stock market's rise has boosted private wealth, real disposable income is higher. ''The question is whether the consumer is going to spend.''

''From a political point of view, growth is important,'' says Penner. ''The longer it takes for growth to get going, the higher unemployment will go. If delayed into next year, the chance of going over 11 percent unemployment is very great. As remarkably patient as people have been with unemployment, that would be intolerable.''

President Reagan called Republican leaders to the White House Nov. 18 to discuss the Regan and Lewis proposals, and Republican strategy for the lame duck session that begins Nov. 29 and ends the week before Christmas.

Some of his supporters, however, want to see something grander than lame duck session maneuvers.

''To recover from the loss in the election, from the perception he may not be able to effectively manage the country's affairs, with the Democrats stronger in the House, he (Reagan) needs a new offensive,'' says one of his Washington backers. ''But I see a circling of the wagons more than a break through in the lines.