Just as a bipartisan coalition was gaining the upper hand against Sen. Edward M. Kennedy's civil rights bill, White House chief of staff John Sununu late last week bought on to a new version that raised both the menace of racial quotas and new Republican doubts about Bush policy.

''Kennedy was waiting for the White House to blink, and Sununu blinked,'' an angry business lobbyist told us. One senior administration official privately described the situation as ''incredible, appalling.'' Confidence in President Bush's pledge against a civil rights bill with quotas was shaken, as Sununu and Kennedy negotiated one-on-one with Republican senators excluded from the talks.

That's part of the overriding Republican concern that the White House always will flinch when facing remorseless Democratic pressure. Despite Sununu's new veto threat as the Senate wrangled yesterday, Republicans were still highly dubious about what the White House might do before the battle ends.

The civil rights fight tests Bush's kinder-gentler model against hard-nosed adversaries. Kennedy's bill reverses Supreme Court decisions that undercut government prohibition of racial discrimination in hiring. By bearing the ''civil rights'' label, it is intensely popular. But by forcing employers to set racial quotas or face hard litigation, it is intensely unpopular.

That poses a dilemma peculiar to Bush. On May 17, he pledged to veto any bill containing quotas. But he is loath to risk his high standing among blacks by taking on Ronald Reagan's ''anti-civil rights'' mantle.

Immediately prior to the Fourth of July congressional recess, Sununu seemed on the verge of agreeing with Kennedy to language that the business coalition contended would force employers into quotas -- the same week the president broke his no-tax pledge. On June 29, Sen. Orrin Hatch intervened by telling the chief of staff that the White House was about to sign on to a quota bill. Sununu backed away.

When the lawmakers returned last week, anti-quota senators seemed to be in the driver's seat. A compromise by moderate Republican Sen. Nancy Kassebaum had attracted Sens. Dennis DeConcini, Dale Bumpers, Bennett Johnston and perhaps more Democrats. It also appealed to moderate Republicans such as Sen. Pete Wilson. Not only would the Kassebaum proposal provide a safe civil rights haven but it might generate sufficient votes to sustain a veto.

It was thus a total surprise when on July 12 Sununu entered a meeting with Republican senators and embraced a compromise that Hatch, Kassebaum and others said did not solve the quota problem. ''I think John is being taken for a ride,'' an aggrieved Hatch told us.

But why would Sununu let Kennedy roll him? The conventional wisdom is that Bush has made clear to his chief of staff that he simply does not want to be put in the position of having to veto a civil rights bill. As chief of staff, Sununu is bound to pursue the Bush agenda.

However, there is another factor: Sununu's special style. The main complaint about him by conservatives is that in his exuberant self-confidence he feels invincible -- in this case, that he can achieve the goal of making a deal with Teddy Kennedy and of splitting him from Ralph Neas and the civil rights lobby. Furthermore, Sununu has come to look on Republican lawmakers as sunshine soldiers who cannot be counted on to stick to unpopular positions.

Kennedy this week submitted language that set off new talks between him and Sununu. Although their talks stalled Monday night, Bush's credibility with his core constituency was undermined.

Hatch and other Republicans see quotas as a rare case where public opinion runs against the civil rights lobby. But the president seems reluctant to charge head-on against Democratic leaders eager to unsheath their partisan knives as the midterm election nears.