The company plans to eliminate about 190 of its more than 1,900 positions worldwide.
That would eliminate the tax for about 99.7 percent of all families, according to lawmakers in both parties.
Over the next five years, the plan would eliminate 30,000 administrative jobs out of about 140,000.
The carrier also plans to eliminate about 2,800 workers from its total force of 83,000.
The House bill would eliminate the need for about half of the private coverage.
The companies said they would eliminate about 4,000 jobs, or 10 percent of their combined work force, over the next three years to reduce costs.
Also, the company would eliminate 1,000 jobs, about 4 percent of its work force.
Already, major American financial services companies have announced plans to eliminate about 30,000 jobs.
The company also announced plans to eliminate 5,000 jobs, about 13 percent of its work force.
It has promised to eliminate about 1,800 jobs before the year 2000.