The first, and more obvious, is that the voters of 2000 prize a candidate who projects authenticity and gravitas and that they are largely unmoved by the advice of other politicians.
The second message to all those Republican leaders who have been embarrassed by the result here -- far more menacing -- is that their candidate, Gov. George W. Bush of Texas, might be incapable of selling himself as a national political leader in the general election in November.
Or, put another way, the lesson from New Hampshire is not just that McCain is strong but that Bush may be weak.
So the first question for the Republican Party today is whether this result is an aberration or the sign of some fundamental flaw in Bush that will allow McCain to overtake him in subsequent contests.
The Bush campaign has no choice but to spin out theories that might reassure his supporters and campaign workers. So it will be said that McCain's startling performance was the freakish result of the independent voters who made up about one-third of the Republican electorate. Or we will be told that things will be different when the campaign reaches states with strong Republican governors such as John Engler of Michigan and George E. Pataki of New York.
The conventional wisdom will be that Bush's huge advantage in campaign money -- he still has more than $30 million on hand -- will make the difference in states in which the campaigns will be heavily reliant on television advertising.
There is a seed of validity in all those arguments. But they do not recognize how dramatically and immediately the landscape has been transformed by McCain's margin here. Although McCain cannot match Bush in cash on hand, he can expect a flood of money in the next two weeks.
At the least, McCain will have enough money to see him through the South Carolina and Michigan primaries that are the next critical battlegrounds for the Republican candidates.
More important, however, McCain now will become the hottest political celebrity in the campaign. The Arizona Republican suddenly will be the star player on the three major television networks, the cover boy for the newsmagazines. And he has shown here that he can thrive under that kind of press attention.
Bush's weakness here shows, moreover, that he will have to make a fundamental change in the nature of his campaign. The notion that a politician cannot lose by promising bigger tax cuts has been refuted. Exit polls here showed voters preferred McCain's more modest tax reduction with more money to pay down the debt.
The campaign here did not turn on issues, however. It turned on the image McCain projected as a plain-spoken political heavyweight running against a youthful scion of a famous family. Political veterans here rolled their eyes Saturday when Bush brought his father and mother to a rally at Milford, then sent the 2,000 potential voters home without making even a brief speech.
And the pros muttered among themselves when Bush spent the weekend being filmed by the television crews driving a snowmobile and sliding down a hill with some kids. By contrast, McCain continued holding those 114 town meetings at which he answered question from all comers.
To a lesser degree, the close contest in the Democratic primary was a similar verdict on the way most Americans regard political leaders. Vice President Al Gore enjoyed the support here of Gov. Jeanne Shaheen and every other Democratic leader of high position in the state, as well as the backing of the liberal icon in these parts, Sen. Edward M. Kennedy of Massachusetts.
He also was supported by a sophisticated organization run by people who had been successful here in the past.
But those credentials were flimsy enough to allow Bill Bradley to avoid the kind of blowout Gore and his advisers had hoped to score here. The Gore campaign managers were so cocky that they had instructed their state campaign chairmen to contact the leading Bradley backers to set up a dialogue for after the voting.
Their hope was that if Gore won by an impressive margin here, the Bradley supporters would join in urging the challenger to abandon his campaign in the interest of party unity. A plan had been written by the Gore campaign to roll out endorsements from the so-called super-delegates to the convention and from some interest groups not yet officially on board.
The message, of course, was to be that Gore's nomination was inevitable.
Now, the vice president and the Democratic establishment that united behind him know there is an element of doubt about the eventual outcome -- one that cannot be resolved before March 7, the date of the big primaries in California, New York, Ohio and several other states.
There is one significant difference between the situations in the two parties -- the position of the two challenging candidates within their parties.
Although Democratic leaders are overwhelmingly behind Gore, most of them would live with Bradley as the party nominee. The same is true of labor unions and such constituent groups as black voters. Differences between the candidates have been matters of style rather than substance.
McCain's situation is quite different. In the Senate most of his Republican colleagues -- Fred Thompson of Tennessee and Chuck Hagel of Nebraska are the exceptions -- view him with considerable bitterness because of the leading role he has taken on campaign finance reform and anti-tobacco legislation. Senate Majority Leader Trent Lott has made no secret of the animosity he feels toward the senator from Arizona.
The results from New Hampshire suggest this animosity may be more of an asset than a burden for McCain with the voters. But all those governors and senators who have endorsed Bush will do whatever it takes to prop him up as the campaign moves on.