A new congressional budgetary offensive is to be launched on the House floor today to fund major military and domestic projects President Carter has been trying to halt.

The $6.8 billion fiscal 1978 supplemental spending measure is likely, before it's all over, to include funds for production of the controversial B-1 bomber and already contains money to build the Clinch River breeder reactor project President Carter wants halted.

The supplemental also now contains the money President Carter proposed for accelerated cruise missile research and development as an alternative weapon system to the B-1 bomber.

Congressional advocates of the $110 million-a-copy B-1 served notice yesterday that they will sponsor an amendment today to put the bomber into production.

"It's a whole new ball game." Rep. Robert L. F. Sikes (D-Fla.), ranking Democrat on the Defense Appropriations Subcommittee, said last night in confirming that he and his House allies will reopen the drive to restore $1.4 billion for the B-1.

In approving the supplement bill for House floor action, the House Appropriations Committee struck out funds President Carter wanted - including $6.3 million to help settle 15,000 Indochinese in the United States and $160,000 to give White House National Security Affairs Adviser Zbigniew Brzezinski four additional high-salaried assistants.

Supplement appropriations are sought by the Administration or added to the bill by House or Senate action after the regular money measures for departments and agencies have cleared Congress and have been signed into law. They have often been used in recent years as back-door spending devices for proposals that might not survive the normal budget process.

In the case of the B-1, the administration put its 3-vote margin in the House in jeopardy by announcing, after the President canceled the bomber, that it was considering converting the F-11 (once known as the TFX) into a strategic bomber. Until that happened last week it was expected that Congress would comply with the President's wishes on the B-1.

Afterward, however, House Appropriations Chairman George H. Mahon (D-Tex.) said the President "muddied the waters" by expressing an interest in a new bomber - possibly the modified F-111 - capable of penetrating Soviet defenses.

Similarly, the Clinch River reactor money was put in the supplemental bill when Carter's opposition relayed the 1978 funding authorization. House and Senate conferees have agreed on an $80 million funding level for Clinch River in the Energy Research and Development Administration budget.

As recently as last week the President criticized Clinch River, and his aides say he may veto the ERDA authorization bill because the reactor project is in it.

But such threats are not expected to change the minds of House members who appear ready to approve the money even though the authorization has not yet been signed into law.

The supplemental contains more than $500 million for other fiscal 1978 Pentagon programs, many of them designed to support the accelerated cruise missile program upon which the president embarked.

On its own initiative, the House Appropriations Committee added $152 million for the purchase of additional F-14s, the $20-million-each Navy carrier plane which has been criticized as too costly.

Among other items in the bill:

$117 million to pay for cargo preference allowances to U.S. shippers - representing the extra cost of using more expensive American tankers, as required by law, to bring at least half the oil purchased for the strategic petroleum reserve.

$4.5 billion to be spent over a 10-year peiod on grants for waste treatment plan construction around the country. The first such grant program of $18 billion was approved in 1972.

$17 million to locate the new Department of Energy at the James Forrestal Building and other government sites.

$4 million supplement for the Agriculture Department to provide grants to low-income elderly persons in rural areas for home improvements.

At the same time the supplemental spending measure was short of funds which would have been required to administer new taxes included by the President in his energy program. The action reflected the House committee's skepticism that those portions of the energy would be enacted.

Also excluded from the measure was $160,000 sought by the administration to hire four experts at GS-16 and above, to handle "East-West relations, development economics, general policy analysis and congressional liaison."

In pressing for the funds a National Security Council spokesman said policy analysts work an average of 66 hours a week, with the support personnel costong "nearly $10,000 in overtim pay per period."