THE STRUGGLE in the White House over trade policy and machine tools seems to be moving to a climax. A small Florida toolmaker called Houdaille Industries is pressing its campaign for protection from Japanese competition through a new legal tactic. Houdaille argues that the Japanese manufacturers are a cartel subsidized by their government, and in retaliation it wants President Reagan to revoke the 10 percent investment tax credit for any Japanese tools bought by an American company.

It's an extremely dangerous idea. The evidence supporting the charge of cartelization is not persuasive. As for subsidies, the Japanese machine toolmakers evidently get some help. But it is also true that most manufacturers in most countries, including this one, get some help from their governments. The case is important precisely because this kind of limited subsidization is widespread. If Houdaille can invoke it to get protection, an endless list of further and larger industries is also eligible.

The Houdaille petition seemed to be moving toward the president's desk at one point last week. But some of the better economists in the Executive Office Building caught it and managed to send it back to the office of the trade representative, Bill Brock, for further analysis. That's a good sign.

Perhaps sensing a growing resistance, the National Machine Tool Builders' Association has now launched a parallel appeal for protection through the more conventional device of import quotas. The toolmakers have been badly hurt by the long recession. Beyond that, they do not seem to be competing well against foreign producers. Abandoning any more elegant argument, the Machine Tool Builders simply assert that they are essential to the arms industry and national defense. Therefore, they say, they are entitled to protection regardless of the cost to the rest of American industry.

And that's where the burden would lie. Take, for example, the American aircraft industry. A major exporter, it is running into increasingly stiff competition in foreign markets. If protection for the tool manufacturers makes sophisticated machine tools more expensive, it will raise costs for other American companies, such as the aircraft manufacturers. Jobs saved in the machine tool industry would be more than offset by jobs lost in the aircraft industry.

President Reagan had it exactly right when he went after protectionism in a speech earlier this month in San Francisco. "What the proponents of this bunker mentality never point out," he said, "is the costs of protectionism for one group are always passed on to another group down the line." He was speaking of protectionists in general. The next step is to apply that sound principle to the machine tool case.