Senators who oppose President Carter's pardon on Vietnam war draft dodgers failed in an effort yesterday to hold a vote on a resolution expressing disapproval of the pardon. The procedural vote on whether to bring up the resolution sponsored by Sen. James B. Allen (D-Ala.) was 53 to 43, seven short of the needed 60.

Majority Leader Robert C. Byrd (W.Va.) said he had urged Carter to issue his pardon early. Byrd, who opposed a pardon, declined to say whether his advice was based on the possibility of strong Senate opposition.

The President told interviewers from Associated Press and United Press International Sunday that he was not surprised by the reaction to the pardon.

"It is a proper thing to do. It is one that I feel very much at ease with. It is something that should have been done. I was very grateful to be the one to do it," Carter said.

A pardon for draft evaders was one of his campaign promises.

Carter said the study he had ordered of deserters and men with less than honorable discharges will "try to decide which groups can be handled in categories, which ones should not be changed at all, and which ones would be best handled on a case-by-case basis."

Carter said: "Groups that might be handled on a category basis would be alcoholics, or perhaps those who were mentally incompetent to complete the basic training, or perhaps those who didn't adequately support their families for some reason or another."

Of others "who have committed more serious crimes involving drugs or perhaps an act of violence," Carter said, "it would be my inclination to let the military handle those on a individual case-by-case basis, depending on the evidence presented."

Those who received undesirable discharges, he said, might be given the next higher discharge - a general discharge.

Those who received bad conduct or dishonorable discharges would not be considered for such an upgrading, he said. "They have been tried in a military court. They have been convicted of a crime."

Meanwhile, the Wisconsin American Legion is seeking to expel Carter from the veterans' organization because of the pardon.

"We are going to Washington Feb. 20 for the national midwinter conference of the American Legion and will ask the President be permanently barred from membership," said Robert Wilke, adjutant general of the state organization.