A plan to hire Louis Harris to poll the public on major national issues on behalf of the House of Representatives is quietly being scuttled Republicans worried about its $2 million annual cost.

The poll was the idea of Majority Deputy Whip Bill Alexander (D-Ark.) who says the purpose is to "coordinate and assimilate" in "a national way" the polling efforts some individual members already make.

Alexander and he has been talking to Harris with the approval of House Speaker Thomas P. O'Neill (D-Mass.) and Minority Leader John Rhodes (R-Ariz.). Alexander said the only conditions O'Neill set were that participation be voluntary and the polling be bipartisan and nonpolitical.

Rhodes said he had talked to Harris and tentatively endorsed the idea, but now the plan had "grown out of all proportion." Rhodes added: "Our people won't approve it."

Rep. Mickey Edwards (R-Okla.) who was detailed by Rhodes to work with Alexander on the plan, said part of the purpose of the polling would be to get "unbiased information" to counteract the influence on the House of single issue groups and special interest lobbying.

Alexander and Edwards agreed on these details of the plan.

Harris would draft questions on six or eight national issues, half to be chosen by Democrats and half by Republicans. He would poll 40 congressional districts, initially, and if members were satisfied with the results, would expand the operation. The results would be public information, according to Alexander.

Edwards said Harris estimated that it would cost $2 million a year.

Edwards said that besides the cost, there was concern that Harris, would, in effect, become the pollster for the House.

"There would be a great deal of prestige attached to being the pollster of the house," he said.

Edwards said he discussed the proposal with Rhodes and Republican Campaign Committee chairman Guy Vander Jagt (Mich.) and they had called Harris and told him: "We don't want to go so far as to tell you the idea is dead, but we have serious trouble with it."