Congress adjourned for its Fourth of July holiday yesterday leaving unresolved a marathon feud with the White House over a supplemental money bill to keep parts of the government running for the current fiscal year.

The House wound up the week of pro-forma sessions in a brief morning meeting without dealing with the latest Senate-passed compromise version of the supplemental. Most members had been on vacation throughout the week.

The Senate went home in early evening after passing a job training act to replace the expiring Comprehensive Employment and Training Act.

Both houses will return on July 12 to be confronted with several more rounds of argument and votes on what is officially dubbed an "urgent" supplemental appropriation bill, two versions of which already have been vetoed by President Reagan.

The House failed to override President Reagan's first veto and it is likely that it will make its first order of business an attempt to override the second one.

When still a third formula was found faulty by Budget Director David A. Stockman, Senate Republicans quickly patched together a compromise and sent it--No. 4--to the House this week. That one irritated both Democrats and Republicans in the House who had not been consulted in advance by the White House. They refused to summon members back from vacation to consider it.

The stalemate left several agencies nearing depletion of funds to pay salaries. More than 900 employes of the inspector general's office in the Department of Health and Human Services were scheduled to be furloughed today, but when the congressional negotiations failed Secretary Richard S. Schweiker said yesterday that enough funds could be transferred from other programs to keep them employed until July 30.

Employes of the Merit Systems Protection Board, however, were not so lucky. "There's no way around it," said board spokesman Lon Anderson. "Our entire staff of 310 people are being put on half time starting Tuesday until whenever Congress gives us some remedy."

White House spokesman Larry Speakes, traveling to California with the president, raised the possibility that Congress should pass a fifth bill to fund only agencies in immediate danger of running out of money.

Under this plan, the House would return from recess to approve the measure and then take up the pending fourth version after July 12 to fund the other agencies.

"It's our judgment they the House would come back from vacation" to approve No. 5, Speakes said. "We would hope they would."

But a return from the recess appeared to be highly unlikely.

The job training act, passed 95 to 0 by the Senate yesterday, authorizes money to continue the Job Corps and to help train disadvantaged youth and dislocated workers. Most of the funds would be channeled through state governments.

It would replace the much-criticized CETA program, which had emphasized public service jobs. CETA is scheduled to expire in September.

The bill passed yesterday carries no price tag, but is expected to cost about $3.8 billion, the amount specified in the congressional budget resolution for a job training program. The House Education and Labor Committee has approved a different version which would cost $5.4 billion but it has not reached the House floor.

The Senate bill calls for the establishment of training programs designed by private industry and local elected officials.

The Senate spent much of the afternoon arranging a time schedule for debating, some time after the recess, a major crime control bill reported out by the Judiciary Committee.

That bill contains changes in the right of defendants to plead insanity as a defense. But under the agreement reached yesterday, the insanity provisions will be stripped out and considered later after the completion of committee hearings on the implications of the jury verdict which found John W. Hinckley Jr. not guilty on grounds of insanity in the shooting of President Reagan.