THE WHITE HOUSE mail, President Reagan argues, is proof that the voters support him on the next round of budget cuts. His appeal to the country on Thursday evening, in his view, will once again turn the issue in Congress. He dismisses the jaundiced response of the financial markets. But most people will look for more reliable indicators of support than either organized mail campaigns or the prices of stocks and bonds. How about the warning signals that the president is getting from experienced politicians in his own party?

Gov. Richard Snelling of Vermont, a conservative Republican and chairman of the National Governors' Association, was in town last week to pay a call on Mr. Reagan. His message was that, yes, he still firmly supports the president's goals, but the cuts are coming too fast, with too little preparation. The country, in his view, needs to be careful in working out adjustments -- particularly in programs like welfare and medical care for the poor -- that will be, at best, wrenching.

Some of the conservatives -- those, at least, who run for public office -- are getting anxious about the pattern of tax cuts for people with high incomes and spending cuts at the expense of people with very low incomes. Congress also knows that the president is mistaken in thinking that $16 billion in new cuts will hold the 1982 deficit to his target. The more likely figure is twice that, or a little more.

The past month's confusion and quarrelling within the administration over these latest spending proposals has also had an effect in Congress. They have demonstrated to even the least perceptive and most obedient of congressmen that the administration no longer has a coherent and carefully organized plan for budget reductions. It is improvising and patching as it goes along. In a series of decisions that begin to have the look of desperation to them, it is now going after the famous social safety net that, earlier in the year, was supposed to be inviolable.

The budget question is now coming to a crisis --but it is an artificial crisis, owing its severity to a tax cut this summer that was too large. Mr. Reagan is quite right in saying that the budget deficit has to be reduced. Interest rates will never come down as long as deficits are going up. But there are two ways to balance a budget. One is to keep cutting spending. But how about another look at taxes?

The process throughwhich the country has been going is a healthy one. A year ago, a large majority of Americans believed that public spending had got altogether out of hand. They believed, with some justice, that a lot of money was being wasted, and that a lot of loud little lobbies were living all too well at public expense. A campaign of rigorous and unsentimental budget-tightening was indicated. But it has been clear from the beginning that there would come a moment when most Americans said, "Enough."

After going through all of those suspect spending programs, one by one, discarding some and shrinking others, there would come a point at which peoplebegan to feel that they were down to the minimum that represents the traditional American idea of social responsibility. The country now seems to be approaching that point, a little earlier than Mr. Reagan and his tax-cut bill anticipated.

It is not the American tradition to let children go hungry in order to create tax subsidies for real estate speculation. It is not the American tradition to cut off medical aid to sick people because the administration is running short of money, and can't bring itself to clamp down on tax evasion. Since Mr. Reagan is concerned about the deficit, it is time for him to give the same kind of attention to the revenue side of the budget that he is giving to spending.