A bipartisan Senate health bill would reduce the deficit by almost $4 billion over the next decade without significantly affecting the number of people who have coverage, the Congressional Budget Office found in a report released Wednesday.

Sens. Lamar Alexander (R., Tenn.) and Patty Murray (D., Wash.), the bill’s co-sponsors, said the findings strongly bolster the case for their legislation. But a standoff between the White House, which wants more provisions to undo the Affordable Care Act, and Democrats, who reject such...