The bill to raise the cost limit on the Central Utah Project was batted back to the House by the Senate late Tuesday night.

The measure has been sent back and forth across the Capitol like a badminton shuttlecock as Congress moves toward adjournment. Tuesday's action removed a "killer" amendment the House had added to the measure last week. If the House approves, the bill could go to President Reagan for his signature before Congress folds its tent for the year.As approved by the Senate, the CUP would get authority to spend $45 million more next year than the old ceiling, if Congress appropriates the money. The project was about to exceed its authorized limit and construction would be shut down without the boost.

The bill would also provide $15 million in compensation funds for the Strawberry Water Users Association for surface rights to 56,775 acres of land to be transferred to the Forest Service, and $3 million for rehabilitation of pasture lands in the Strawberry Valley.

The compensation funds would be taxable, according to Sen. Jake Garn, R-Utah, who piloted the CUP bill through the Senate.

The amendment the Senate defeated would have relieved local interests in Nebraska from $125 million in cost-sharing on a Missouri River streambank stabilization project of the Corps of Engineers. The administration objected to that proposal, hung on the CUP bill by Rep. Dick Cheney, R-Wyo.

The Senate left intact amendments adjusting the boundary of the John Muir National Historic Site in California, and barring San Francisco from expanding its water and power dam in the Hetch Hetchy area of Yosemite National Park.

The Muir site is in the district represented by Rep. George Miller, chairman of the House Water and Power subcommittee.