TUESDAY'S CAUCUS made it all but official: next month, Sen. Baker of Tennessee will formally become the first Republican Senate majority leader since the Eisenhower years. For Mr. Baker as well as his colleagues, this means a really new role: for the first time in a quarter of a century, they will be responsible for making things happen in the Senate. That's very different from helping to make things happen or conditioning them or stopping them altogether.

During the four years he has served as minority leader, Mr. Baker has frequently been able to produce a consensus among his party members in the Senate. But he would probably be the first to agree that forging a "reactive" consensus among 41 minority members is easier than attempting to organize a comprehensive legislative agenda for enactment into law among 53 individuals of diverse interest. And legislative minorities have the added advantage, in resisting the initiative of the majority, of being able to tweak, have fun and be slightly reckless. At least the Republicans get one unusual break in assuming new Senate responsibilities. More than half of the Senate Republicans have been elected in the past two years, so at least half of them do not face the additional complication of reeducating themselves out of the ingrained decades-old ways acquired in opposition.

What will be the Senate Republicans relations with the new Republican president? Clearly, Sen. Paul Laxalt of Nevada occupies a unique position just now. Sen. Laxalt, who effectively squelched any potential conservative Republican revolt against Sen. Baker by agreeing to nominate him for the majority leadership, enjoys the friendship and confidence of Mr. Reagan. In addition to his good relations with the president-elect, he is a popular and respected member of the Senate. So he should be able to play a constructive role as go-between. In this, he could turn out to be either Sen. Baker's most valuable ally or his most formidable problem, depending on their own relationship in the next few months.

Those arrangements, like the operating relationships reached with the House Democratic majority and among the Senate Republicans themselves, will determine to a considerable degree the success of the Republican stewardship of the Senate. Despite glowing post-caucus talk of "spirit of cooperation" and "enthusiasm," the priorities of Sen. Jesse Helms are not those of Sen. Charles Mathias, and there is a lot of political distance between various members of that party in the Senate.

Leadership, the art of compromise and effective coalition-building, will be required for both the Republican administration and the Repubican Senate to produce a record, among other things, to take to the country in two years. Sen. Baker, a beneficiary of the Democrats' failure to do just that, probably understands that fact better than anyone else in Washington.