Prime Minister James Callaghan was hunting today for the handful of votes he needs to keep his labor government in power.

If he cannot find them, he will go down to defeat Wednesday on a general motion of confidence demanded by Margaret Thatcher, leader of the opposition Conservatives.

A defeat would force Callaghan to call a general election next month. Thatcher's Tories would be heavily favored to win. The government would be in the unenviable position of seeking votes at a time of raging inflation, high unemployment and stagnant industrial output.

But the immediate hurdle is Wednesday's confidence vote, and one of the most knowledgeable Labor figures tonight said bluntly, "The artihmetic looks bad."

Callaghan can count on only 308 of the 310 Labor members of Parliament. Reg Prentice, who resigned from his Cabinet, is expected to vote against. Tom Litterick, a backbencher, has been disabled with a heart attack.

In addition, Callaghan can expect the support of Ulster's two Catholic members, Gerry Fitt and Frank McManus. But that gives the government a base of only 310, four short of the necessary minimum in a house where 628 can vote.

The 278 conservatives, dreaming of electoral victory and the first woman prime minister in British history, will vote solidly against. So will 11 Scotish and three Welsh Nationalists who blame the government for failing to enact a bill giving their provinces a measure of local government. A pair of Labor breakaways, the scottish Labor Party twosome, will probably join the Nationalists for the same reason.

There are 10 Ulster Protestant members, and at least nine are hostile to Callaghan. The tenth is Enoch Powell, a onetime Tory minister who broke with his party and nurses deep grudges against its leaders.

But his Protestant colleagues blame the government for the renewed spate of Irish Republican Army murders and bombings and see no prospect of getting back their old Ulster ascendancy under a Labor government and suspect the government of leaning toward Catholics.

This group is full of mavericks, however, and Callaghan has faint hopes of peeling a few away.

The government's best chance of survival should have rested with the 13 Liberals. But their young new leader, David Steel, 38, has openly proclaimed that the Liberals will support Callaghan only if he makes a public pledge to shift Labor's legislative course.

It is hard to see how Callaghan could comply without risking a revolt from his party's left wing. Political observers of all stripes have said that Steel has pitched his terms too high for a deal.

The prime minister met both Steel and the leaders of the Ulster Protestants, James Molyneaux and Powell, today but there was no reason to believe the equation had changed appreciably.

In the end, Callaghan's best hope appears to lie in pyring loose a few Liberals dubious about Steel's firm line and some Ulster Protestants.

The crisis is not unexpected. For months, the best-informed here have been saying that the minorty Labor government could come undone only over the devolution bill, the home-rule measure for Scotland and Wales. Labor has a working majority over the Tories, but it needed to prevent them from making common cause with the Nationalists.

Last month, 42 Labor members either abstained or voted against a motion to limit debate on the home-rule measure. That all but killed it for this year. Moreover, it drove the Scottish and Welsh Nationalists firmly into opposition, determined to bring the government down.

Even if Callaghan squeaks by on Wednesday, his government faces a bleak-future. It would have to negotiate an endless series of political road-blocks thrown up by opposition groups.

The prime minister had hoped to hand on for another 18 months or so and postpone an election until Britain's economic fortunes had taken a clear turn for the better. But whatever happens Wednesday, that strategy now seems destroyed.

The Callaghan government has been one that must enact what it least likes and could not enact what it most wants.

If it stayed in power, Labor would have to satisfy Scottish and Welsh aspirations for self-government and pass a devolution bill. For ideological and parochial reasons, many in the party are hostile to the home rule bill.

In much the same way, the government must, to fulfill treaty pledges, enact a measure providing that the British voters - not Parliament - shall choose deputies to the Common Market legislature at Strasbourg. Many in labor are also hostile to the European Market and fear any drain of sovereignty from Parliament.

On the other hand, the party's activists would dearly love to redistribute income more equitably with a tax on wealth. But Callaghan does not have the votes.

Similarly, the typical Labor member of Parliament would like to legislate a measure of "worker democracy," forcing corporate boards open for union members. Here, too, however, Callaghan would have little chance of getting such a bill through.