Rep. John B. Anderson of Illinois, chairman of the Republican Conference, said yesterday the House should adopt a rule preventing members from sending tapes of their floor speeches home to local media.

During the last Congress the House began radio coverage of its proceedings. The House-operated coverage is to be made available to radio reporters on request, but Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) also allowed members to order recordings of their own speeches for distribution to media in their home districts.

That "not only distorts floor proceedings by encouraging more members to speak, but could raise the charge that the broadcast system was being used as another incumbent-protection device at taxpayers' expense," Anderson said.

He said this problem could soon get worse, as the House also begins televising its proceedings under a House-controlled system.

"Broadcast coverage should be made directly available to the media on request but should not be permitted to be duplicated and spoon-fed to the media by individual members," Anderson said.

Anderson's complaint was one of many leveled yesterday as Republican leaders criticized House Democrats' proposed rules changes.

Minority Leader John J. Rhodes of Arizona charged that the rules would "give the majority leadership near dictatorial powers" over the order of business, virtually destroy meaningful debate, and prevent Republicans from offering cuts to spending totals.

Republicans made suggestions of their own for rules changes, but the proposals are not expected to be approved by the Democratic-controlled House. The Democrats will offer their changes as a package without allowing amendments when the new Congress opens on Monday.

Rhodes and Anderson complained about rules changes Democrats agreed on in a December caucus.

Rhodes called "most dangerous" a change that would forbid amendments to alter the total in a budget resolution. This would prevent consideration of the kind of across-the-board cuts that Republicans almost succeeded in getting adopted last year -- unspecifically demanding a lower spending figure for the budget as a whole. Rhodes said preventing these total cuts "subverts the whole budget process."

Republicans also objected to the power the Democrats gave the speaker to defer and cluster votes on bills. Anderson said it will allow House members to spend Mondays and Fridays out of town while bills are being debated. It would "encourage absenteeism" and "permit manipulation and abuse of the timing of the votes," Anderson said.

Rhodes said Republicans are "formally calling for an oversight Congress," reviewing already adopted programs and regulations, as opposed to a Congress that passes new laws and programs.

He called for a rule making oversight by committees mandatory, for passage of so-called "sunset" legislation, and for a one-house congressional veto of agency and department rules and regulations.