A House-Senate conference committee began work yesterday on a compromise version of the fiscal 1980 congressional budget resolution, with prospects for a long -- and possibly bitter -- fight over a series of key issues.

Because of conflicting floor-votes in both chambers, the panel stayed in session yesterday only for a token organizational meeting. However, committee leaders planned to push this morning for action on specific proposals.

The two houses have major disagreements this time on several highly controversial matters, including widely differing proposals for defense and domestic spending and a flap over whether to cut back already-enacted money bills.

The House has approved a resolution calling for $548.2 billion in spending for fiscal 1980, which began October 1, and a deficit of $28.9 billion, roughly in line with what President Carter has proposed.

The Senate's proposal would set total spending at $546.3 billion, with a deficit of $31.6 billion -- too high, some leaders feel, to win approval by the budget-concious House.

The conference panel is under pressure because the two houses already have missed the September 15 deadline for finishing the resolution that is prescribed by the five-year-old congressional budget process.

Under this procedure, Congress approves tentative tax and spending targets each spring and then revises them in the fall to turn them into binding ceilings. The fall measure is supposed to be passed by mid-September.

Congressional sources were pessimistic yesterday about how quickly the conference panel could finish work on the measure. Both sides believe they have strong mandates from their respective houses.