The Consumer Product Safety Commission -- faced with deep budget cuts proposed by the Reagan administration, business antagonism and internal division about the future structure of the agency -- yesterday opened a congressional fight that will chart the panel's future.

Acting CPSC chairman Stuart Statler told a House subcommittee that the agency already is operating on a "bare-bones, no frills" budget and that the 30 percent budget cuts proposed by the administration would damage CPSC's ability to monitor dangerous products.

Statler, a Republican, also told the panel that the budget cuts would reduce consumer confidence in both government and the products the commission regulates.

"Ultimately, the public's confidence in the safety of consumer products will be undermined, and its confidence in the viability of the federal program to protect against unreasonable risks of injury will be misplaced," Statler said.

A House subcommittee on health and the environment is considering two bills: one introduced by the panel's chairman, Rep. Henry Waxman (D-Calif.), that would restore the commission's funding for the next three years, and another by Rep. James Broyhill (R-N.C.) that adopts the cuts proposed by the administration.

The Waxman bill would grant the agency $45.2 million for fiscal 1982 with increases to $47.2 million and $49.5 million for the following two years. The Broyhill bill would cut the projected CPSC budget of $47 million to $33 million next year and $35 million for the 1983 fiscal year.

The CPSC is charged with monitoring the safety of products ranging from drug bottles to toys. Statler said the CPSC has prevented hundreds of deaths and hundreds of thousands of poisonings of children because of a standard for safety caps on aspirin, for example.

Statler also said "several thousand cases of cancer will not occur" as a result of CPSC actions involving chemicals, while a rule on lawn mower safety, when it becomes effective next year, will prevent an estimated 60,000 injuries a year.

The fight over the agency's future will take place in Waxman's subcommittee, which has opened the first reauthorization process for the agency in three years. Senate hearings will begin later this spring.

If last year's bitter political fight about the Federal Trade Commission's reauthorization and yesterday's critical testimony from business groups involved in CPSC matters is any indication, the CPSC may be in for a difficult time in Congress.

Further complicating matters is Statler's suggestion that the commission might be better run by a single administrator, rather than by a five-member commission. Statler is opposed on the proposal by three other CPSC members.

But the CPSC members all said the large cuts would be disastrous. Commissioner David Pittle said the cuts, which would reduce the agency's engineers, economists and injury analysts by 25 percent, "seem designed more to hamper the ability to function than to effect a real savings for the nation's economy.