(CNN) — With Hillary Clinton behind in New Hampshire and holding on to a narrowing margin over Vermont Sen. Bernie Sanders in Iowa, new CNN/ORC polls in Nevada and South Carolina suggest Clinton holds strong support in the two states that could prove to be a firewall for her.

Clinton has the support of 50 percent of those who say they are likely to attend the Democratic caucus scheduled for February 20 in Nevada — which plays host to the first debate among the declared Democratic candidates on Tuesday and is the first state to elect delegates after Iowa and New Hampshire.

Sanders follows at 34 percent, then Vice President Joe Biden at 12 percent, with the rest of the field garnering less than 1 percent support.

Among those who say they are likely to vote in South Carolina’s primary, set for one week after Nevada’s caucuses, Clinton holds a larger edge, 49 percent to Biden’s 24 percent, with Sanders at 18 percent and former Maryland Governor Martin O’Malley at 3 percent.

Should Biden decide to sit out the race for the presidency, Clinton’s lead grows in both states. In South Carolina, a Biden-free race currently stands at 70 percent Clinton to 20 percent Sanders with O’Malley holding at 3 percent, and in Nevada, Clinton gains 8 points to 58 percent, while Sanders picks up just 2 points and would stand at 36 percent.

In South Carolina, Clinton’s advantages stem largely from Sanders’ unpopularity with black voters, who made up a majority of Democratic primary voters in the state in 2008, the last time there was a competitive Democratic primary. Back then, black voters broke 78 percent for Barack Obama to 19 percent for Clinton.

In the new poll, 59 percent of black voters say they back Clinton, 27 percent say Biden and just 4 percent for Sanders. Among white voters, Sanders has the edge, 44 percent to 31 percent for Clinton and 22 percent for Biden. Without Biden in the race, it’s a near-even split among whites, 48 percent Clinton to 47 percent Sanders, while blacks break 84 percent to Clinton and just 7 percent would back Sanders.

These two states, along with Iowa and New Hampshire, are the only ones permitted by both major parties to hold primaries or caucuses in February, and the outcome of the contests in these early states can make or break a presidential campaign.

Iowa’s caucuses will happen first, and a recent NBC News/Wall Street Journal/Marist poll in the state finds Clinton 11 points ahead of Sanders there, a narrower margin than she holds in most national polling. New Hampshire’s primary follows, and several recent polls there, including a CNN/WMUR poll released in September, have found Clinton trailing Sanders by a significant margin in the state.

Clinton’s stronger support in Nevada and South Carolina could bolster her campaign heading in to the large batch of “Super Tuesday” contests set to be held on March 1.

In both Nevada and South Carolina, Clinton holds double-digit advantages as the candidate who would do the best job handling the economy, health care, race relations, foreign policy and climate change, and is broadly seen as the candidate with the best chance to win in 2016 (58 percent say so in South Carolina, 59 percent in Nevada).

The margins between Clinton and Sanders narrow when it comes to which candidate is most honest and trustworthy (in South Carolina, 35 percent say Clinton, 27 percent Biden, 21 percent Sanders, in Nevada, 33 percent Sanders, 32 percent Clinton and 22 percent Biden), and in Nevada, on who best represents Democratic values (44 percent say Clinton, 37 percent Sanders) and understands the problems facing people like you (42 percent Clinton, 39 percent Sanders).

The four other candidates tested in the polls — former Rhode Island governor Lincoln Chafee, Harvard professor Larry Lessig, O’Malley and former Virginia senator Jim Webb — lag well behind Clinton, Sanders and Biden on the issues and attributes tested. None of them top 3 percent on any of those questions.

The economy is the clear top issue in both states, with 45 percent in Nevada and 43 percent in South Carolina calling it the most important issue in determining their vote for presidency next year. Health care and social issues follow in both states, though South Carolina voters are more apt to say health care is key than Nevada caucus-goers (29 percent health care, 10 percent social issues in South Carolina, 16 percent for each issue in Nevada).

Clinton’s biggest issue advantage comes on foreign policy (she’s up 38 points over Biden in South Carolina and 30 points over him in Nevada), while the margins are narrower on the economy (47 percent Clinton, 24 percent Biden, 18 percent Sanders in South Carolina, 46 percent Clinton, 31 percent Sanders, 15 percent Biden in Nevada) and climate change (44 percent Clinton, 22 percent Sanders and 21 percent Biden in South Carolina, 41 percent Clinton, 30 percent Sanders and 16 percent Biden in Nevada).

While Sanders and Clinton have been sparring over the economy for quite some time, both foreign policy and energy policy have earned attention from the two campaigns recently. Sanders has highlighted his opposition to the Iraq war in 2002 as a foreign policy credential, while Clinton declared her opposition to the Keystone XL pipeline.

The CNN/ORC polls were conducted by telephone October 3-10. A total of 1,009 South Carolina adults were interviewed, including 301 who said they were likely to vote in the Democratic presidential primary. In Nevada, interviews were conducted with 1,011 adults, including 253 who said they were likely to participate in the Democratic presidential caucus. Results among likely Democratic voters in South Carolina have a margin of sampling error of plus or minus 5.5 percentage points, for Nevada Democratic caucusgoers, it is 6 points.

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