THE FIRST THING to be said about the Iowa Republican caucuses is that Bob Dole won a handsome victory. He may have had a regional advantage in this farm state, but his support was broad and deep and he proved he could assemble a strong organization. His margin over his recent days' sparring partner George Bush was a solid 2-1. The second thing to be said is that Pat Robertson showed once again the ability to mobilize a large constituency of followers and get them to vote. His 25 percent was impressive, but he must do better to win in caucus states, and he must break through in primaries -- he pointed to the March 5 South Carolina contest -- if he is to be the serious contender for the nomination he says he is.

If Mr. Robertson is looking ahead past New Hampshire to South Carolina, and Mr. Dole now has the luxury of looking in several places for his next win, Vice President Bush is the man on the spot. If he wanted to contrive a grueling test of his ability as a politician, he could hardly have done better than his surprise third-place finish in Iowa, which puts him under the severest of pressure to win in New Hampshire. He can argue that Iowa is atypical, that its Republican electorate is the most anti-Reagan in the land, that Mr. Dole's advantage of being from the Farm Belt and Mr. Robertson's ability to muster thousands of enthusiasts to caucus sites won't make much difference in future contests, most of which are primaries in nonfarm states. These are all pretty good excuses, but the uncomfortable fact remains. In Iowa 100 percent of the Republicans who turned out in the caucuses knew who George Bush was, and 81 percent didn't vote for him. On a clear night the vice president of the United States could muster only 20,000 of Iowa's 1.6 million voters to support him -- less than two-thirds as many as backed him, as a lesser public official, in 1980.

In New Hampshire Mr. Bush is on more favorable ground. He has been leading in polls there for months, though his lead seemed to dwindle late last week and may now be gone. President Reagan is popular and Mr. Bush's pledge not to raise taxes, period, is good politics in a state where governors are expected to "take the pledge" not to raise state taxes. Mr. Robertson has little natural constituency in New Hampshire, and his enthusiasts make less difference in a high-turnout primary than in a low-turnout caucus.

The temptation will be for Mr. Bush to try to win by pushing New Hampshire's no-tax button and by emphasizing, as he did Tuesday morning, that he was born in Massachusetts, grew up in Connecticut and summers in Maine; "I'm one of them," as he said in Nashua. But Mr. Dole is running New Hampshire ads featuring his spending freeze -- at least as plausible a low-tax strategy as Mr. Bush's sweeping promise -- and Jack Kemp, whose ads have been striking a spark, can argue that he is a more reliable tax-cutter than anyone. What Mr. Bush needs to do, as David Broder observes on the op-ed page today, is to set out the affirmative case why he should be president. What will he do? How will he do it? What problems come next? How can they be solved? New England neighborliness and faithful service as a popular president's acolyte will not be enough, we should think, for victory in New Hampshire; and even if they are, they won't be enough elsewhere. If George Bush wants to be president, he's going to have to do more than scuffle with a network anchor and try to bop his principal competitors around. He must persuade people he's right for the job.