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A strong showing by Rubio in New Hampshire, building on Iowa, would put him in very good position to expand his base in the next round of primaries. A weak showing by a number of his competitors, like Chris Christie, would probably result in their dropping out of the race. If Rubio falters Tuesday, then the governors -- Christie, John Kasich and Jeb Bush -- may survive in the race longer.

The most notable aspect of New Hampshire is the strong presence of independent voters. They are sizable in number (about 40% of the state's voters are "undeclared," with about 15% being truly independent) and they are able to vote in whatever primary they want because the parties don't have the kind of restrictive rules that exist in many other states. New Hampshire's Republican voters are less religious and less conservative than in many other states, so even the non-independents are different from the Iowa caucusgoers. 

While the party vote will still matter most in New Hampshire despite the conventional wisdom about the state, this pocket of voters is a very important signal as to how the candidates can do in tightly contested states down the line.

That means this primary will provide the first real sense of what independent voters are thinking when it comes time to vote, and of the views of Republican voters who are not quite as right wing as the tea party. For Cruz, it will mean this is a chance to demonstrate that his brand of extreme conservatism is still capable of building the coalitions that will be essential to an election victory. 

For Trump it is a chance to prove he is the only candidate who has the potential to reach out beyond the narrowing constituency that Republicans have depended on. Rubio and others are thirsting for a strong show of support from independents to prove they are the only candidates who can gain a serious hearing from the public and form a center-right coalition.

Democrats are just as interested in that independent vote. In a funny way, Trump and Sanders, two very different candidates who have thus far appealed to their respective party base, are now competing for this same group of voters. Sanders, campaigning in his home territory, is looking to show voters and party stalwarts that he can be something more than a left wing radical storming the gates. He wants to attract a vote from independents sizable enough that he can make the argument that his focus on the broken political process will resonate throughout the country. 

Although Clinton keeps urging voters to be realistic, the kind of criticism that Sanders raised about the political process during the recent debate is a critique that has widespread appeal in an era when Americans don't trust government or government officials. Clinton, seeking to solidify her credentials as the only electable candidate running for the Democrats, would use a strong showing to marginalize Sanders as a fringe candidate. Both of them want to show that a Democrat can do much better drawing independent voters than anyone among the Republicans.

The most troubling aspect of the Iowa caucuses for Sanders was that Clinton did well with older voters, women and moderates, pretty much the perfect recipe for winning the nomination. Sanders, on the other hand, derived much of his strength from the support of younger voters, who are more erratic and unpredictable in elections. 

If Sanders can't broaden his reach, it will mean that his long-term path to victory will depend on a very precarious base of support that is unlikely to carry him far. Sanders faces another challenge in that New Hampshire has very low poverty rates and the economy is pretty strong, counteracting his emphasis on inequality and the economic woes of the 99%. The actual data from the voting, if it replicates Iowa, will also continue to stir the doubts that exist among many Democrats nationwide that the Sanders campaign is anything but a protest vote from the young and alienated parts of the electorate, something that is important to the process but not something capable of producing victory. Should Sanders draw on a broader coalition in New Hampshire that goes beyond the youth, Clinton would find herself in an even more defensive position going into the next round of state competition. 

Much of the discussion after Iowa centered almost entirely on the candidates and the issue of momentum, a natural choice given that this is the first contest of the election season. But primaries are also important because they offer an opportunity to start gauging which issues are important to the electorate and which issues will have little impact.

Thus far polls in New Hampshire have shown that voters are most concerned about terrorism and foreign policy, as well as immigration and drug policy. One interesting aspect of the contest will be to see if those polls show a continued focus on those issues or if concern about the economy is mounting. This is crucial for Republicans who need to campaign against a Democratic administration at a time of recovery.

In particular, the underlying anxiety amid economic recovery will be on the minds of voters. In New Hampshire, the economy is doing quite well, but polls show voters don't have much confidence in their situation. As one mental health counselor told The New York Times, "We're better than average economically, but not everything is milk and honey." 

New Hampshire will open the window a little further into what this campaign is going to look like in the next few months and which candidates are in the strongest position to make a run for the nomination. While the winner might very well lose the bigger battle, the contest itself gives us insight into how voters are thinking of the campaign.