VOTERS DON'T write the federal budget; that's what they hire politicians for. So a poll of voters' opinions on budget issues must be interpreted carefully. Take this month's Post-ABC News poll. It shows, for example, that only 22 percent favor defense spending increases, while even fewer -- from 4 to 20 percent -- support cuts in domestic programs such as Medicare, Medicaid and student loans. Since the president's budget increases defense and cuts the latter, you might conclude that the voters are solidly against it.

But there is something to the argument, usually made by administration acolytes, that voters are using Mr. Reagan's programs as a baseline. They understand that defense has gone up a lot in the Reagan years, and, happy with that, see no need for it to go up much more; they have the sense that domestic spending has been cut, and are cautious about cutting it further. And certainly they come out on Mr. Reagan's side on tax increases. By a 68- to-30-percent margin, they agree that taxes should not be increased to cut the deficit.

Even granting all that, however, the poll does not support the White House position that the people really support the president's budget, even if the politicians don't. Mr. Reagan's operatives are quick to argue that well-connected lobbyists and well-positioned congressmen have kept in place many programs that the public generally doesn't particularly want and for whose continued existence there are only the flimsiest of arguments. True enough. But added all together, these programs don't amount to much. The real dollar cuts in Mr. Reagan's budget come in things such as Medicare, Medicaid, housing and student loans.

When you know that, you understand why that budget doesn't have very many votes on the Republican side of the aisle, let alone among the Democrats. Would you like to run for reelection next fall -- pick any state or district you like -- on a platform of big cuts in medical care and student loans? Not surprisingly, few Republicans are being advised by their pollsters and consultants to do so. The Post-ABC News poll shows, as other polls have shown, and as the results of the political process over the past five years have shown, that the public doesn't want big cuts in these programs.

It won't be easy to reconcile that desire with the public's aversion to tax increases. The polls give little guidance, since voters have no clear sense of the magnitudes of money involved. But reconciling these conflicting goals is the unpleasant business the voters hired the president and Congress to perform, however much both sometimes seem to want to deny it.