THE prospect of revamping the nation's tax system may be gathering momentum. GOP lawmakers intent on overhauling the Internal Revenue Code appear increasingly likely to make tax reform a major issue in the 1996 presidential campaign. They claim they are tapping into a deep well of discontent over the way the US government collects taxpayer dollars. Congressional leaders and presidential hopefuls, such as House majority leader Dick Armey (R) of Texas and Senate majority leader Bob Dole (R) of Kansas, are pushing a host of alternatives, including a flat tax that would require everyone to pay at the same rate, a national sales tax, and a value-added tax targeted at consumption and designed to promote savings. The White House dismisses most of the proposals as gimmicks that would fall heaviest on the poor, hurt business, and reduce government revenues. Americans are weighing in with opinions of their own. One barometer of public sentiment is the early response to the Commission on Economic Growth and Tax Reform, a group set up three months ago by House Speaker Newt Gingrich (R) of Georgia and Mr. Dole. ''We literally cannot open the mail or respond to the phone calls, the faxes, and the e-mail fast enough,'' says Grace-Marie Arnett, the commission's executive director. Chaired by former Cabinet member Jack Kemp, the 14-member commission is poring over the 9,000-page federal tax code and developing its strategy to weed the system of rules, regulations, and red tape that strangle the nation's economic growth. Ms. Arnett has guaranteed the public access to the commission: If a person can restrict his or her complaints and prescriptions for change to one written page, she will forward it to members. During the last week in August - a slow time for any office - she received hundreds of letters. A groundswell of support for major tax reform? ''We're just beginning to make people's radar screens, and what we're hearing is that people feel personally oppressed by the system,'' Arnett says. Yesterday in Washington, the commission held its eighth of 13 public hearings planned for this year. Meetings have already been held in Boston; Omaha, Neb.; Charlotte, N.C.; and Palo Alto, Calif. They have been attended by tax-reform activists like Nancy Mitchell. ''People want a tax system that is simple and fair,'' says Ms. Mitchell, an economist and vice president of the Washington-based Citizens for a Sound Economy, a group promoting a flat tax. Since January, her organization has commissioned public opinion experts to hear what people are thinking about the issue. ''A typical response,'' she says, came from men and women assembled in Cedar Rapids, Iowa. Representing various income levels and ages, the group strongly supported dismantling a system in which ''special-interest lobbyists are paid $500 an hour to belly up to the trough to get in their clients' deductions.'' As voters in an early-primary election state, these ''middle American'' taxpayers in Iowa are important political indicators. ''New Hampshire gets a megaphone every four years,'' Mitchell says of the first state to vote in the presidential primaries. Intent on helping to mold that message, her organization sent tax missionaries fanning out to other early primary states, including Arizona, Texas, New York, Florida, and Michigan. ''The American people will expect a presidential candidate to talk about tax policy,'' Mitchell says. ''Clinton will be forced into the debate; the only question is when.'' Treasury Secretary Robert Rubin insists Clinton must resist jumping in with his own plan just ''because a bunch of other people are doing it and because it's fashionable.'' While opponents are busy floating trial balloons, the chief executive is grounded in common sense, says Mr. Rubin. The tax-reform proposals may be attractive at first glance, he says, but ''none of these are clearly better than where we are today.'' And all of the tax-reform proposals fail to meet four basic criteria, he argues: no damage to economic growth and savings, fairness so the growing income disparity is not widened, simplicity, and doesn't add to the deficit. Still, radical reform is not an issue that will quickly fizzle out, says Arthur Hall, senior economist at the Tax Foundation. But its success is ''contingent on two things: what the budget looks like and who's the president in 1997,'' Mr. Hall says. ''In order to push ahead, there needs to be a president who clearly cares about tax reform.''