The three independent civil service unions that are opposing the president's plans to "reform" the government's personnel system have an uphill fight in Congress and with the taxpayers.

Administration officials have done an excellent job of selling the reform package. It is designed to give management more control over the hiring, firing and reward system the government now uses for its million-plus white collar civilians.

Public opinion polls show that the average taxpayer believes that government workers are overpaid and under-worked, and enjoy job benefits and tenure that are unmatched by workers in the private sector.

Being against the "reform" of the civil service system is a tough assignment.

Although they are mortal enemies on the organizing front, the National Federation of Federal Employees (NFFE), the National Treasury Employees have buried the hatchet - temporarily - to fight the "reform" plan. (Congressional hearings on it resumes next week before the House Post Office-Civil Service Committee.)

While they lack the money, membership and clout of AFL-CIO's American Federation of Government Employees, the three independents do have certain strengths and connections that will help them on Capitol Hill. AFGE president Kenneth T. Blaylock has given qualified support to the "reform" plan, contingent, on getting administration backing for a labor-management law suitable ot the AFGE.

Some of the pluses the independents have are:

National Federation of Federal Employees: NFFE claims to be the biggest of the independents, and has more members in the upper levels of the civil service (in terms of grade and pay) then the AFL-CIO union. NFFE also has excellent grass-roots contacts with important small town editors and local 'opinion molders' and its restraint in asking for the right to strike has pleased many members of Congress.

National Treasury Employes Union has an excellent legal team that has pulled off some big-money miracles in court. NTEU is the outfit that challenged, and beat, President Nixon when he delayed the start of a federal pay raise from October until January. NTEU took the president to court and won back pay for nearly a million federal workers.

National Association of Government Employees has Kenneth T. Lyons and his many connections. Friends are tha name of the game in this town, and Lyons - whose power base is in Boston - has them.

He is a long-time friend of retired House Speaker John McCormack, and used his access to the speaker's office to have hearings scheduled, and to win or block legislation that NAGE favored or opposed. He also is close to the present speaker, Thomas P. O'Neil (D-Mass.), and that won't hurt a bit.

In addition, Lyons has ties to Rep. Joseph Moakley (D-Mass.) who is on the powerful Rules Committee. His union has retained the Washington law firm of former Rep. Graham Purcell (D-Tex.) who enjoys good contacts with conservative members on Capitol Hill who don't normally warm up to unions.

The independents contend that the Carter "reform" plan is just a rerun of the Nixon administration's attempts to make the bureaucracy more responsive to political managers.They feel the "reforms" would eliminate employee rights in dismissal actions, and give politicians a stranglehold on the top-levels of the career civil service.

In the months ahead, the independents will try to sell Congress and the public that their opposition isn't directed against genuine reform, but exists because they see the proposal as a threat to the merit system of govenment.

The trick will be to persuade enough people that their opposition isn't a knee-jerk reaction to new ideas, and that they aren't out to obstruct genuine improvements in a civil service system that certainly could stand improvement.