Rhodesia is planning to launch a major lobbying campaign beginning in January to convince the U.S. Congress to lift economic sanctions on the beseiged country and recocgnize elections scheduled in April to establish a moderate, black majority government here.

Whth 75 percent of Rhodesia now under martial law and the guerrilla war closing in on the capital itself, white Rhodesian authorities appear to be counting heavily on making a diplomatic breakthrough with the United States to save the present white-led transitional government.

While this may seem abroad to be grasping for last straws and largely irrelevant to the outcome, the Rhodesians feel that any sign of support from Congress or the U.S. government will be a tremendous morale booster at home and encourage other countries, such as South, africa and some in Europe, to follow suit.

"Let's face it," said one high-ranking white government official, "Britain is a spent forece and what really counts for us now is Capitol Hill."

Britain, the former colonial power here, has never accepted the white Rhodesians' unilateral declaration of independence in 1965 that has led to the current political impasse and nationalist guerrilla war. Repeated Rhodesian efforts to reach a constitutional settlement and gain diplomatic recognition from various British governments since then all have ended in failure.

The U.S. government also has refused to recognize Rhodesia's independence. But there is a substantial faction in Congress known to be sympathetic to the Rhodesian cause and supportive of efforts here to establish a moderate black government in which whites would still exercise considerable economic and political power.

The Carter administration, together with the British Labor Party government, has been attempting since March to convene a peace conference attended by both leaders of the Rhodesian government and the Africanand communist-backed nationalist guerrillas fighting to topple it. Combined British-American deplomacy, however, so far has failed to achieve this goal, leaving the United States in a dilemma, without a clear policy alternative.

There is every indication that a major struggle will take place in the coming Congress between the Carter administration and supporters of Rhodesia first over bypassing the economic sanctions imposed on the rebel country by the United Nations in 1965-66 and then over whether to recognize the April 20 elections, which the nationalist guerrillas are certain to boycott.

Sources here and in Washington believe that one of the chief strategists for the Rhodesian lobbying campaign will be John Carbough, a top aide to the conservative Sen. Jesse Helms (R-N.C.). He is reported to have been the mastermind behind much of the maneuvering this past year to get Congress to pass pro-Rhodesian amendments.

Another person who may well play a preminent role in the Rhodesia campaign is Donald De Kieffer, who worked as a lobbyist for the south African government until the recent information scandal there.

It is not known for sure here whether De Keiffer has been hired officially by the Rhodesian government to lobby on its behalf on Capitol Hill, but he is known to have visited here in Mid-October and met with some resident Americans who are active in promoting the Rhodesian cause.

Rhodesian authorities seem extermely optimistic about the prospects of forcing the Carter administration to change its Rhodesia policy through a high-powered lobbying campaign.

Already, they feel the visit to the United States in October of Prime Minister Ian Smith and his three black colleagues in the ruling Executive Council here was a big step forward in selling the American public on Rhodesia.

While most U.S. newspapers seem to have concluded that Smith gained little by his visit, strategists of Rhodesian foreign policy estimate it to have been "a 60 to 70 percent success."

They list as positive gains in their effort to sway the American public and Congtess Smith's agreement at the end of his two-week stay to attend a British-American sponsored peace conference "without preconditions." They feel the effect of this was to make the government here appear "reasonable" and willing to talk while the guerrilla leaders and some of their key African backers were backing off from going to a conference on these terms.

Moreover, Smith's accetpance put the State Department very much on the defensive in trying to get leaders of the guerrilla Patroitic Front, Joshua Nkomo and Robert Mugabe, to attend a peace conference.

Perhaps most important in their eyes, Smith and the three black internal leaders met one of the two conditions laid down by Congress last summer for eventual U.S. recognition by agreeing to talk to the guerrilla leaders. The other condition was the holding of "free and fair" elections for black majority rule.

Also regarded here as good tactics during the Smith visit to the United States were the Rhodesian raids on nationalist guerrilla camps deep into Zambia and Mozambique. The attacks, Rhodesian strategists feel, showed the American public that contrary to wide belief, the Rhodesian armed forces are not on the verge of military defeat and still pack a powerful punch.

Other positive gains, according to these Rhodesians, were the vast number of personal contacts that Smith and his colleagues made on Capitol Hill; the overall "good" exposure they got on all the major television networks; and the strenthening of their political base among conservatives in Congress.

Finally, the very fact that Smith was finally allowed into the United States is being interpreted here as tantamount to de facto recongnition of the biracal transitional government.

As these Rhodesian foreign policymakers analyze the political landscape in the new Congress, they see Rhodesia on the threshold of a breakthrough. They calculate, for example, that around 42 senators will now be favorably disposed to lifting economic sanctions, or at least to buying Rhodesian chrome -- as the United States did in violation of U.N. sanctions during the last years of the Nixon-ford administrations.

Congressional sources say this callculation may not be too far off. If so, the Rhodesian lobbyists only need to win over a handful of additional senators to get the Senate to agree on lifting sanctions wholly or partly.

As for the House, the Rhodesians now feel they could swing a vote in their favor on the sanctions issue withoug too much trouble. Without disagreeing outright with this assessment, congressional sources say pro-Rhodesian sentiment in the new House is still very difficult to measure.

Whatever the precise count, the Rhodesians seem extremely confident of making serious inroads into the Carter administration's policy of holding the line on giving any U.S. backing to the Rhodesian transitional government over the coming months.

But U.S. officials counter that much will depend upon how much time and energy the White House is willing to sepnd on upholding its present Rhodesian policy. At the very least, they assert, the administration should be able to hold the line until the April elections in Rhodesia.