Stung by public criticism, the House is moving to force its members to tell the public how much postage-free mail they send and rein in those lawmakers who abuse the privilege.

New limits on how much mail House members can send out free were made part of a $2.2 billion bill that provides money to operate Congress in the 1991 fiscal year that began Oct. 1. The bill was approved 292-117 Sunday and sent to the Senate.The bipartisan compromise limit on Congress' franking privilege, adopted on a voice vote, was a sign that lawmakers are nervous about their low standing in the public eye.

With that in mind, and with elections just 16 days away, the House also voted $76 million in spending cuts before giving final approval to the appropriations bill. Included in the cuts was a proposed $50,000-per-member increase in staff salary accounts.

Members were so sensitive about spending money on themselves that they spent hours Sunday sparring over whether to spend $500,000 on modular furniture and $350,000 to renovate the House beauty shop.

The furniture was nixed, but the beauty shop renovation was preserved after female House members argued that its old wiring represents a safety hazard.

Despite appearances, the ceilings on free mail were set high enough to avoid affecting most lawmakers. And some of the other cuts are expected to be restored in negotiations with the Senate this week or in a supplemental money bill next year, staff sources said.

Left unscathed was a whopping increase in House members' salaries - from their current $96,600 to $125,100 effective Jan. 1.

Under the new mail limits, each House member would be given an allowance sufficient to send three first-class mailings to each residential address in the district, an average of $178,000.