In a desperate bid to save this year's housing bill, House Democrats yesterday agreed to cut the measure's funding by a third, bringing it into line with Senate proposals and appropriation bills that already have passed.

The bill, which originally called for spending $23.6 billion, had been attacked by Republicans as a "budget blockbuster," and yesterday's reduction to $15.6 billion was an admission by Democrats that the higher figure had no chance of becoming law.

Rep. Henry B. Gonzalez (D-Tex.), who offered the reduction amendment, said he did so "not because I believe this level of effort is sufficient--for clearly it is not--but because it is the most realistic alternative."

The cuts were big enough to bring over wavering Democrats and many moderate Republicans to pass the amendment on a voice vote. However, some fiscal conservatives indicated that they will vote against the measure when it comes up for final passage, expected today.

Major reductions in the Gonzalez amendment were: Community Development Block Grants, down $1 billion to $3.5 billion; low-income assisted housing, down about $5 billion to $9.9 billion; rural housing programs, down about $700 million to $3.2 billion, and operating subsidies for public housing, down $100 million to $1.45 billion.

However, the measure retains a provision that would put the government back into the construction of low-income housing, producing, according to Gonzalez' figures, about 200,000 units a year. It would require subsidized tenants to contribute 25 percent of their income toward their rent, down from the 30 percent required by current law.

The House narrowly rejected, 208 to 206, an amendment by Rep. Chalmers P. Wylie (R-Ohio) that would have forbidden any community that imposes rent control on new construction from participating in the new rental housing production program.