GREENVILLE, S.C. -- That George Bush hasn't quite finished pinning down the South and is muscling hard to do so was underscored two hours before his performance here when his two South Carolina kingpins dropped into Jimmy Snyder's Mercedes-Jaguar showroom.

Ex-governor James Edwards and ex-representative Tommy Hartnett did not come to kick tires. They came to corral Greenville City Councilman Snyder, described by Edwards as ''a lost sheep.'' He is a rare establishment Republican in this state not on the Bush bandwagon. Worrying about the vice president's electability against some bright young Democrat, Snyder backs Rep. Jack Kemp. He was not budged by his visitors.

What bothers Snyder was confirmed that night at ''Ask George Bush,'' the forum most favored by the vice president's strategists. That's where, theater-in-the-round style, he answers tame questions from invited guests. Pledging loyalty to President Reagan, he failed to seize on enthusiasm engendered among deeply conservative South Carolina Republicans by two disparate Americans: Oliver North and Robert Bork. Bush sings the Reaganite lyrics, but moderately; it's right-wing words but without music.

He may not need the music here. This state is the jewel in the southern crown fashioned for Bush by national campaign manager Lee Atwater, a South Carolinian. The state's primary, which comes in solitary Saturday splendor March 5, could build Bush momentum for Super Tuesday southern primaries three days later and protect him from shortcomings in the early Midwestern and New Hampshire tests.

Atwater's passion for front-loading campaigns with organization, money and big names looks obsessive in his home state. His hand was seen when Hartnett switched to Bush after he had promised to back Kemp. Atwater may also keep Sen. Strom Thurmond from supporting Sen. Robert J. Dole. A close Atwater associate, Gov. Carroll Campbell, is expected to join Bush next year.

In comparison, the opposition looks feeble. Dole has growing business support, but his hit-and-run stops here build no base. Kemp's backers grumble about his inattention. Pat Robertson is organized, but only among charismatic Christians, who cannot get much above 18 percent of the vote.

Those few hardy dissidents denying Bush inevitability -- such as State Sen. David Thomas of Greenville -- find life uncomfortable. What Thomas calls ''the liberal country-clubbers'' opposed his renomination and threatened his money supply the moment he endorsed Kemp. Now, with not one Kemp phone call to buck him up, Thomas may slide out of the presidential race.

Jimmy Snyder is subject not to pressure, but to argument. Outside his showroom, he heard Edwards contend that Bush in presidential qualifications compares with South Carolina's revered Jimmy Byrnes. But Snyder said no. Earlier, not wanting to say no directly to Bush, he had advised Hartnett not to let the vice president telephone him.

Snyder's obstinacy is explained by what happened at ''Ask George Bush.'' Asked to describe the Reagan administration's unfulfilled agenda, the vice president talked about budget and trade deficits, the ''horrors of illiteracy,'' ''outdoor recreation'' and ''reduction in tensions'' internationally. He volunteered nothing about contra aid, the Bork confirmation, economic growth or abortion. Softball questions on Iran-contra hearings and AIDS were fouled away.

Nevertheless, Bush's guests departed quite delighted. Thomas, his support of Kemp dimming (''a malaise has come over his campaign'') labeled the performance ''like a personal chat with the vice president.'' These are the Republican elite, respectful of re'sume' and authority.

There will be more than the elite voting March 5. With no competing Democratic primary and no party registration, nobody can predict how many or, more important, who will go to the polls. Could 200,000 white, conservative, uncontrollable South Carolinians steal the jewel from the crown Lee Atwater has fashioned?

Possibly, if some candidate provides a reason to vote. Former senator Paul Laxalt, backed by textile mogul Roger Milliken, is making a blue-collar appeal of protection. If Dole roars out of the Midwest and New Hampshire, he could be formidable.

But Kemp, consigned to fourth place by Bush backers, may have the best chance to build grass-roots strength. His organization is taking shape. Ex-U.S. attorney Henry McMaster, last year's U.S. Senate nominee, will become Kemp campaign chairman, with his campaign manager, Gene McCaskill, handling details. Greenville Mayor William Workman will help. They and Jimmy Snyder bother the well-oiled Bush machine, for this is one state the vice president cannot afford to lose.