Carter administration brass hope, and expect, to win tentative Senate approval of his multimillion-dollar bureaucratic pay reform package even before a less receptive House begins hearings.

The issue of who gets the bill first may have a major bearing on proposed pay changes for white and blue-collar federal workers. Under the plan, more than a million civil servants - including about 340,000 here - would have their pay linked to the going-rate for similar jobs in local industry.

Insiders say the Senate Governmental Affairs Committee may begin pay reform hearings sometime after July 4. It will be September, at the earliest, before the House Post Office-Civil Service Committee even begins subcommittee sessions on the Carter plan.

The Carter plan would remove military personnel from the system now used to set raises - each October - for most federal workers. Under it, white collar employes, pay would be determined by comparison of actual salaries and government fringe benefits matched against counterpart "total compensation" in industry. Increases would be adjusted locally, according to prevailing rates paid for the same jobs in industry.

Although the Senate and House committees have the same function - oversight of the bureaucracy - they go about it very differently. And with a different cast of characters. The Senate committee has broader interests. Members, with a couple of exceptions, are often bored with government "housekeeping" chores. And few of them have strong ties with federal, postal or retiree groups.

The House Committee has closer ties to government unions and has generally been more sympathetic to bills improving the lot of federal employes. And it has been able to do some important foot-dragging on legislation that would cut salaries and fringes of government employes.

Ironically, President Carter got better cooperation from House Republicans on the House committee than from Democrats on his successful plan for civil service reorganization. Democrats on the House committee have stronger local ties to federal groups. And many of them are angry, feel snubbed or left out of contacts with the White House on a variety of subjects - from energy to civil service changes.

Important subcommitte leaders on the House side have shown no reluctance to whack the White House without fear of political fallout. Reps. Bill Clay (D-Mo.) and Patricia Schroeder (D-Colo.) have big federal constituencies, and strong labor ties. Both are sympathetic to complaints from union's that Carter is unduly antibureaucrat. Rep. Gladys N. Spellman (D-Md.) is expected to handle the pay reform bill in her subcommittee. Many federal workers, and unions, are suspicious of the contemplated changes and alleged savings that would come out of future raises. And Spellman, representing a major bedroom community of Washington, counts lots of federal workers - white collar and blue collar - among her consituents.

Administration officials would like the earliest possible action on civil service pay reform. But they suspect the House committee will delay it - for both political and scheduling reasons - as long as possible. So they are counting on the Senate side to give them a great political and psychological leap forward in its earlier hearings.