The House yesterday passed $3 billion in supplemental appropriations for this fiscal year made necessary mostly by the recession.

Sent to the Senate, the money bill contains $1.9 billion for higher-than-expected unemployment benefits, and an additional $443 million to enable states to hire more staff to process claims and help people find new jobs. Congress had cut back these funds for state unemployment offices last year.

The bill also would increase the lending authority of the Commodity Credit Corp. by $5 billion; the CCC, to which farmers turn when prices are low, has used up its present authority.

The administration had requested the unemployment and CCC money, but it opposed an additional $123 million to help poor people pay fuel bills.

Helped along by northeastern Republicans who opposed President Reagan's cuts in the program last year, the Democratic House approved the extra fuel assistance 354 to 62. The new funds boost the fuel-aid total to $1.8 billion this year.

Debate was partisan. House Speaker Thomas P.(Tip) O'Neill Jr. (D-Mass.) set the tone, saying the administration's opposition to the fuel assistance and its delayed endorsement of funds for the unemployment offices proved it was "insensitive to the problems of average working families."

While Republicans Delbert Latta of Ohio and Robert Walker of Pennsylvania argued that the recession began under a Democratic administration, Democrat David E. Bonior decried the 16 percent unemployment rate in his home state of Michigan, declaring, "It's time this administration spent less time with blue blood and more time with blue collar; less time with black tie and more time with black unemployment; less time at receptions and more time on the unemployment lines."

The closing of unemployment offices in several states just as the jobless rate is rising gave the Democrats another chance to blast the administration's budget cuts. "We are here because the administration's economic policies have brought us the highest unemployment since the Great Depression," said Rep. David R. Obey (D-Wis.). Silvio O. Conte (R-Mass.) said it was not the administration's intent in last year's cutbacks to force the closing of unemployment offices.

On fuel assistance, however, moderate Republicans, many of whom fear that their support of the Reagan cuts last year will hurt them in this year's elections, lined up to endorse the additional funds. Declaring that 21 million households were eligible for fuel grants, while only 8.5 million would get help, Rep. Joseph M. McDade (R-Pa.) said, "People out there have to make a decision to heat their homes or to eat; it's that bad."

In Maine, Rep. Olympia Snowe (R) said, 13,000 households have been denied fuel grants because of cuts which have also reduced the average amount each family receives from $600 to $350. Rep. Thomas Coleman (R-Mo.) said natural gas prices have risen dramatically this year and "a lot of people can't meet their present gas bills."

Opposition to the fuel assistance was led by Rep. Bob Livingston (R-La.), who said 16 states have transferred the fuel funds into other block grant programs. The House passed by voice vote an amendment sponsored by Rep. James T. Broyhill (R-N.C.) to prohibit such transfers--and to prohibit grants after May 31, so that heating funds aren't used for air conditioning.