President Reagan's campaign to reduce government spending has produced an ironic twist so many letters are flooding congressional offices in support of the president that the House postmaster wants to spend $240,00 extra on new employes to handle the mail.

"We need help," Postmaster Robert V. Rota lamented. "We're working around the clock, except Sunday."

Roto this week asked the House Administration Committee to appropriate funds for 20 more clerks, supplementing a staff of 100, to handle what he says are 500,000 pieces of mail a day. At this rate, he estimated, his office will receive approximately 300 million pieces of mail this year, twice what it handled last year.

The crush of mail began soon after Reagan outlined his economic recovery plan in a nationallly televised address to a joint session of Congress and urged citizens to write their legislators.

"It's unbelievable," Roto said. "There's no way humanly possible we can handle this tremendous mass volume."

A House Administration subcommittee is expected to discuss Rota's request next week, according to a committee spokesman. The 20 extra grade 2 clerks would cost $12,000 a year each, but Rota is optimistic that the House will grant his request.

"Congressmen are getting their mail two or three day's late," he said. "The speaker [Thomas P. (Tip) O'Neill Jr. of Massachusetts] has been down here. This affects them." Rota has sent a letter explaining the delay to each member.

Although Rota's suggestion has made Rota's life more difficult, he is not bitter. "No matter what the cost, it's the people's right to write their congressman," he said. "It's very important for the members to get their mail."