The Reagan administration yesterday set the stage for a showdown on the Clinch River breeder reactor by sending Congress a plan whereby private investors would put up $150 million to help complete the project while the government would kick in another $1.5 billion.

Under this plan, the government also would guarantee $675 million in privately issued construction bonds, promising to repay them if the breeder, so called because it is intended to "breed" more plutonium fuel than it consumes, is not completed or fails to generate sufficient revenue.

The proposal is certain to become the focal point of an epic struggle in Congress, where an uneasy alliance of liberal Democrats and conservative Republicans contends it finally has the strength to kill the nation's most controversial civilian nuclear project.

It also may become the last hurrah for Clinch River's ardent home-state backer, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), who is determined to guarantee the breeder's future before retiring from the Senate next year.

"This is intended to be the definitive, final consideration of the issue," Energy Secretary Donald P. Hodel said yesterday in sending the plan to Congress. "It has never been a piece of cake. But I think we have a proposal that has a live prospect of going forward."

If the plan is not approved by Congress as a rider to the continuing resolution for fiscal 1984, federal spending on the advanced atomic power plant, in Oak Ridge, Tenn., will cease on Sept. 30.

The federal government already has spent more than $1.5 billion on the project since it was launched in 1970.

More than 70 percent of the plant components have been delivered or ordered. Excavation of the foundation is nearly complete. The Energy Department hopes to obtain a full construction permit from the Nuclear Regulatory Commission by December.

A consortium of private utilities initially pledged $257 million toward the project's original estimated cost of $699 million. A decade of government policy changes and construction delays have pushed this total to an estimated $3.6 billion, but until now private industry has not been asked for more money.

While the new Reagan administration proposal is billed as a plan for "raising $1 billion of private capital" to help complete the Clinch River project by 1989, the proposal only envisions selling $150 million worth of stock to private investors.

Some of the $1 billion would come from interest on the original investment by the utilities.

About $675 million of the "private capital" would be raised through sale of bonds that would be paid off once the breeder begins generating electricity. If for any reason the plant failed to operate or earn sufficient revenue the government would be liable for the bonds.

The report accompanying the proposal said that because of the "long history of political indecision and controversy" surrounding the project, which President Carter tried to kill out of concern that breeders would increase the availability of weapons-grade plutonium, Clinch River is a "high-risk investment."

Thus, to encourage investors to buy stock in the project, the administration would make them partners with the government in a joint venture. Investors would receive tax benefits not just on their $150 million investment but on the "entire private investment," including that represented by the bonds.

Gordon Corey, who headed the utility task force that devised the plan, said that this type of investment ought to be attractive to "large finance company subsidiaries of large companies that have taxable income" that they need to shelter.

"But this is not a Treasury rip-off," Corey said. "It is very easy to say all you are doing is selling tax benefits."

But Corey said the plan was set up with an eye to ensuring that the taxes paid by the bond holders on the revenues they receive are "greater than the tax benefits that will be received by the equity investors."

"So at the worst, from a tax standpoint, there will be a standoff. And at the same time, we will have relieved the Treasury of $1 billion in current obligations," Corey said.