New Hampshire voters on Tuesday night -- Republicans and Democrats alike, as well as the state's famously independent undeclared voters -- delivered a sharp rebuke to politics as usual. The bombastic billionaire Donald Trump easily won the Republican primaries with more than a third of the vote, while independent Sen. Bernie Sanders handily defeated his Democratic opponent Hillary Clinton.

"Together, we have sent the message that will echo from Wall Street to Washington," Sanders told his jubilant supporters in Concord Tuesday night. "And that is, that the government of our great country belongs to all of the people and not just a handful of wealthy campaign contributors and their super-PACs."

After second-place finishes in the Iowa caucuses, the two insurgent candidates claimed their first victories in New Hampshire with the help of voters who are fed up with the establishment. On the Democratic side, about six in 10 voters said they are dissatisfied or angry with the way the federal government is working -- and 70 percent of those voters cast a ballot for Sanders. Among Republican voters, as many as 40 percent said they were not just dissatisfied but angry -- and Trump won 42 percent of the angry voters.

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Trump and Sanders have clearly tapped into a line of voter resentment that crosses state lines and partisan boundaries. It remains to be seen, however, how far that populist energy can carry their respective campaigns.

In the Republican race, Trump is poised to keep dominating: He has a solid lead in polls coming out of South Carolina, as well as an advantage in the sparse polling from other upcoming states. Even so, his victory in New Hampshire illustrated that Trump is still benefiting from a fractured field. The businessman won with 35 percent support, but the candidates competing to represent the establishment alternative to Trump -- John Kasich, Jeb Bush, Marco Rubio and Chris Christie -- collectively took in 46 percent of the vote.

On top of that, CBS News exit polling shows that Republicans were split as to whether or not they wanted a candidate with experience inside Washington or a Washington outsider. But those who wanted Washington experience were divided between a number of candidates, while six in 10 who wanted an outsider voted for Trump.

As the field of GOP establishment candidates narrows, Trump will face a more challenging race. That new dynamic could come into play as soon as South Carolina's February 20 primary, since Christie is already reassessing his campaign. The field of establishment candidates may have narrowed further after the New Hampshire primary, if it hadn't been for Sen. Marco Rubio's poor debate performance on Saturday night.

After his relatively strong third-place finish in the Iowa caucuses, expectations were high for the Florida senator. But by late Tuesday night, with 88 percent of precincts reporting in New Hampshire, Rubio was in a disappointing fifth place.

Even Rubio himself on Tuesday night acknowledged that he screwed up in the debate: "I did not do well on Saturday night... that will never happen again," he promised his supporters.

About two-thirds of GOP voters said that recent debates were an important factor they considered when choosing a candidate to support. Among those who said it was important, 32 percent voted for Trump, while 17 percent voted for John Kasich. Exit polling also showed that Trump (at 23 percent) and Kasich (21 percent) were the big winners among those who decided whom to support in just the last week.

Kasich, at first glance, was the biggest beneficiary from Rubio's poor debate performance. That's likely because of the ground game the Ohio governor built up over months in the Granite State. Yet without that kind of organization in the upcoming primary states, it remains to be seen how Kasich builds on his momentum.

Instead, Rubio's misstep works in part to Trump's advantage by keeping the GOP establishment fractured for longer. It also worked to the advantage of Sen. Ted Cruz, who placed in a respectable third place in New Hampshire after spending relatively little time and money there. Cruz, who ended 2015 with a sizable $19 million in cash in hand, should be capable of competing with Trump for some time. He can do so more effectively with a fractured GOP establishment.

Meanwhile, in the Democratic race, Sanders faces a more challenging path forward than Trump does on the GOP side. As soon as the polls in New Hampshire closed Tuesday night, the Clinton campaign released a memo looking forward to the 28 races that occur in March.

"And whereas the electorates in Iowa and New Hampshire are largely rural/suburban and predominantly white, the March states better reflect the true diversity of the Democratic Party and the nation," the memo said, "including large populations of voters who live in big cities and small towns, and voters with a much broader range of races and religions. The nomination will very likely be won in March, not February, and we believe that Hillary Clinton is well positioned to build a strong - potentially insurmountable - delegate lead next month."

Polls do show that Clinton has an advantage among minority voters. For instance, the CBS News Battleground Tracker out of South Carolina last month showed Clinton winning support from 76 percent of black Democratic voters.

While she attempts to hold onto that coalition of diverse supporters, Clinton is also co-opting some of Sanders' anti-establishment message.

"Sen. Sanders and I both want to get secret, unaccountable money out of politics," she said Tuesday night. "So yes, you're not going to find anybody more committed to aggressive campaign finance reform more than me - Wall Street should never again be allowed to threaten Main Street."