General Services Administration Administrator Jack M. Eckerd, a Republican who has been asked to remain in the administration by President Carter, is considering resigning because of a dispute with the White House over filling no. 2 job in the agency, sources said last night.

Eckerd is resisting pressure from the White House to name Robert T. Griffin, a longtime friend of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass), to the post of deputy administrator.

Griffin, a veteran GSA employee, is currently the special assistant for coordination of the John F. Kennedy Library.

A source familiar with the dispute said Eckerd apparently views it as a test of a pledge he received from the President last Friday that he would be free to choose his own top deputies.

Eckerd's choice for the job reportedly is the GSA's acting deputy diretor, Wallace H. Robinson Jr., a former marine Corps general who headed the Defense Supply Agency.

Eckerd could not be reached for comment yesterday, and a GSA spokesman said the agency had no comment.

White House press secretary Jody Powell was asked about Eckerd's future at his regular briefing yesterday and replied, "I can't say," Powell could not be reached last night.

At his news conference this week, Carter conceded that the White House has made mistakes in not consulting influential congressional leaders about appointments. O'Neill reportedly was angered earlier by appointments of people from his native Masschusetts without his prior knowledge or consent.

The President made one clear attempt to mend his relations with O'Neill last week when he named the speaker's son, Massachusets Lt. Gov. Tom O'Neill, to a commission that is to recommend people for appointment as U.S. abassadors to foreign countries.

Eckerd, an unsuccessful Republican candidates for the U.S. Senate from by President Ford. He has earned Florida, was appointed to head GSA praise during his tenure for reducing political influence in what traditionally has been a patronage-ridden agency.

When the White House announced this week that Carter had asked Eckerd to remain in his job, Powell said that the President "feels it important that the top GSA job not be political."

The dispute over the GSA job is the first clear struggle over political patronage to surface publicity in the Carter administration.

A source familiar with the situation said that Eckerd has made no final decision on his future at GSA and that it clearly will be influenced by the outcome of the dispute with White House officials over the deputy administrator's job.