Congressional budget writers say they expect the House and Senate to give final approval next week to a $1.17 trillion spending plan for 1990 that claims a big deficit bite but leaves most federal priorities unmolested. House-Senate negotiators agreed to the plan - which claims a $99.7 billion deficit reduction - by a unanimous voice vote Thursday after only two short days of public meetings. The few disagreements the two chambers had were worked out behind closed doors. "I don't expect any problems," Senate Budget Committee Chairman Jim Sasser, D-Tenn., said when asked about the prospects for approval.