THE Senate's confirmation of Clarence Thomas to a seat on the Supreme Court came after a political battle of extraordinary ferocity. The bitterness is likely to be long-lived.Some scholars for several years have been worrying about the drastic transformation of the confirmation process in an age when divided government is the rule, and when interest-group intervention in the process has reached such high levels. It remains to be seen whether recognition of this problem will result in a serious, sustained search for remedies. Clarence Thomas probably would not have finally won in the Senate had he not first won and then retained a large measure of public support. However fierce the attack in Washington, at every stage Thomas prevailed in the court of public opinion. The earliest surveys on Thomas last July showed many people unfamiliar with the nominee, but solid pluralities inclined to back him. For example, the ABC News/Washington Post poll of July 1 found 40 percent saying they approved of Thomas's nomination, while just 11 percent disapproved; 49 percent said they didn't know enough to have an opinion. A month or so later, most surveys were finding just over 50 percent of the public in favor of confirmation, about 25 percent opposed. These numbers were to change little, right through Tuesday's final vote. Only one of the 25 to 30 national polls on Thomas's confirmation found more than 29 percent opposed - a Harris survey of Aug. 29-Sept. 2, in which 31 percent opposed Thomas. The Senate hearings on the harassment charges last week grabbed the public's attention in a way no facet of a Court appointment ever did before. Huge audiences followed the televised sessions, and many people debated everything from the merits of the confirmation process itself to the matter of who was and wasn't telling the truth. But, surveys suggest strongly, few people changed their minds about whether Thomas should be confirmed. For example, the ABC News/Washington Post poll of Sept. 15 had recorded 24 percent opposed to Thomas getting a Supreme Court seat. On Oct. 8, after Prof. Anita Hill's allegations had been made public but prior to the resumption of the hearings, the ABC/Post poll found 25 percent opposed, and the next day's survey put opposition at 23 percent. The polls of Oct. 12 and 14, taken while the hearings were going on, reported slightly higher percentages against confirmation, 29 percent in each; the Oct. 14 surv ey found 28 percent in opposition. This series of surveys found some movement in public sentiment from support to "wait and see" and then back again. Overall, though, Thomas's margin was remarkably constant throughout. Surveys by other organizations show much the same thing. Opposition has bounced around in a narrow range since August - from the low 20s to low 30s. And, the size of the plurality favoring confirmation when the hearings ended - on the order of 25 points - was basically what it had been two months earlier. A number of recent polls asked respondents whether they were more inclined to believe Thomas or Hill. Here Thomas was favored, and by almost exactly the same margin as he was on the question of whether he should be confirmed. Most who wanted Thomas on the court found him the more believable; most who wanted him rejected believed Hill. Thomas was strongly opposed by most civil rights organizations on grounds that his views ran contrary to black needs. But at every point a plurality of black Americans favored his confirmation, and in the end a large majority of blacks came down on Thomas's side. Despite perceptions of a "gender chasm" between men and women, most polls showed differences by gender to be modest in the general public. Every survey of the last month has shown clear plurality support for Thomas's confirmation among women. In the past week, as much of the Washington political community gave itself up to a highly emotional display, most Americans stuck soberly to what was their basic judgment all along - that Clarence Thomas deserved confirmation.