The White House warned Senate Republican leaders yesterday that President Reagan can be expected to veto a $13.4 billion supplemental spending bill to pay for assorted governmental operations this year because of objections to the lack of local cost-sharing on water projects.

The administration said it can be expected to veto the measure even though it contains funds that Reagan seeks for antigovernment rebels in Nicaragua.

As a result, Senate Majority Leader Robert J. Dole (R-Kan.) said he may postpone consideration of the bill, which was scheduled for floor action this week.

Asked whether he would push for modifications to meet Reagan's objections, Dole said he assumed that "we'll go back to the drawing boards" on water projects if Appropriations Committee Chairman Mark O. Hatfield (R-Ore.) agrees to do so. However, Hatfield indicated last week that he would risk "confrontation" with the administration rather than back down.

At issue is a four-year administration effort to win Hill approval for cost-sharing arrangements in which local governments and private users would help bear the cost of a multibillion-dollar backlog of harbor, dam and related projects.

When Congress attempted last fall to fund several dozen water projects, Reagan forced it to back down with veto threats.

This apparently is the strategy again this year: to stall projects important to influential members of Congress as leverage to force compromise on long-term legislation to reduce U.S. water-project costs.

Some congressional officials also contend that the administration is using the cost-sharing argument as a "smokescreen" to block water-project funding in general.

Caught in the crossfire is Reagan's high-priority request for aid to the Nicaraguan counterrevolutionaries, known as "contras," who are fighting the leftist Sandinista government in Nicaragua. The House included $27 million in its version of the spending bill; the Senate Appropriations Committee approved $38 million.

The contra funding, in the form of nonmilitary assistance, could be approved separately, but this would entail another fight. Congressional leaders hoped to resolve the issue speedily by tucking it in the supplemental spending bill, which includes funds for continued government operations through Sept. 30.

Water project funding of $63 million by the Senate committee and $72 million by the House represents a down payment on 25 to 35 projects estimated to cost several billion dollars before completion.

They range from a relatively modest flood-control project on Maui in the Hawaiian Islands to major harbor dredging operations in Baltimore and Norfolk that together could cost nearly $1 billion.

Of the 25 projects in the Senate bill, 11 have not been authorized; 15 were not requested by the administration. Cost-sharing plans have been negotiated for 10, although the Senate version would forbid spending until the federal government negotiates cost-sharing arrangements with local officials. Administration officials said this is insufficient because it does not entail permanent reform.

As in the past, many projects in the House and Senate bills benefit the home states of appropriations committee members. Of the 22 Corps of Engineers projects in the Senate version of the bill, 11 are in the home states of the 29 senators on the appropriations panel.

Oregon, Hatfield's home state, would get $6 million toward a $191 million Bonneville lock and dam project, along with a congressional directive to force awarding of a contract for dam construction at Elk Creek Lake.

Other projects include deep-water channel dredging for the inland seaport in Sacramento, Calif.; beach erosion control in Florida; lock and dam construction on the Mississippi River at Alton, Ill., and at Gallipolis on the Ohio River, and ship-channel development at Gulfport Harbor, Miss.