Washington — Other men have tried for the White House from the US Senate. Can Robert Dole (R) of Kansas do it? As a United States senator, Daniel Webster, greatest orator of his day, made history in his famous ''reply to Hayne,'' but he got the electoral vote of only one state, Massachusetts, when he sought the presidency in 1836. Voters preferred the incumbent, Andrew Jackson.
Former Sen. William Borah (R) of Idaho was the best orator in the Senate, and the words ''Borah's up!'' would jam the press gallery. Though his name was often mentioned for the presidential nomination, politicians like those in the famous ''smoke-filled room'' in Chicago, in 1920, picked Sen. Warren G. Harding.
Circumstances today are different; the Senate has been wired for sound and any senator can wear an inconspicuous microphone on a lapel to make his or her delivery as resonant as Webster's.
Right now, Senator Dole, chairman of the powerful Finance Committee, shrugs when the presidency is mentioned. But he has made it official that he is seeking to become Senate majority leader when Sen. Howard H. Baker Jr. (R) of Tennessee retires next year. Dole has contacted 25 to 30 Republican senators, he says, to say that he is interested in the job.
Some political observers surmise that Dole may establish himself as a major power broker, and carry the strategy further than Mr. Baker did - until he hears his name shouted at the GOP convention of 1988 (always assuming President Reagan will run again in '84).
Oddly enough, it is suspected that just the opposite logic guides Baker. Some say he is giving up the majority leadership because he has presidential ambitions, too. He has found it difficult to deal in national politics while carrying on his duties as majority leader, some political observers say.
Dole's first big test as chairman of the Finance Committee came in 1981, and he scored two successes. He pushed through a package of tax cuts for business, and then one for individuals. A former Finance Committee chairman, Russell B. Long (D) of Louisiana, observed then:''Thus far, he's been extremely effective.''
It isn't often that a Republican gets the opportunity: Only twice since Roosevelt's election have Republicans controlled both houses of Congress simultaneously.
Dole is known for his legislative skill and sharp wit. He is a visible and powerful leader who has found himself recently at odds with the White House over the deficit. Democrats will center on the deficit in the presidential election. Dole skillfully increased some revenue features last year. He seeks to harmonize the President's search for tax cuts and his own growing concern over the deficit. Differences between Reagan and Martin Feldstein, chairman of the President's Council of Economic Advisers, are nearing a showdown.
''Time is running out for the Congress and the administration if there is to be action on skyrocketing federal deficits,'' Dole said here. ''With another election season just around the corner, some people apparently believe that action can be delayed until after the 1984 elections. Some even believe deficits do not matter,'' he said.
''The deficit, and its relation to the fate of economic recovery, ought to be at the top of our legislative agenda - not just an excuse for campaign rhetoric. We need substantive action, and we need it now.''