WASHINGTON — The Senate approved a sweeping farm bill Thursday that would cost nearly $1 trillion over the next 10 years, financing dozens of price support and crop insurance programs for farmers and food assistance for low-income families.

The bill passed with bipartisan support, 64-35. It now goes to the House, where it faces a much tougher road because conservative lawmakers want to make deeper cuts in the food stamp program.

‘‘This bill represents significant reform,’’ said Senator Debbie Stabenow, Democrat of Michigan and chair of the Senate Agriculture Committee.

Although the bill is known as the farm bill, the majority of the spending, about $80 billion a year, goes to the food stamp program. The Senate bill would cut $23.6 billion from current spending levels, including about $4.5 billion from food stamps, but senators rejected several proposals that would have made deeper cuts.

The bill also would benefit some Bay State fishermen and catfish producers, according to Senator John Kerry’s office. Two amendments from Kerry would make fishermen eligible for disaster loans and eliminate the Department of Agriculture’s Catfish Inspection Office.