While the 2016 presidential election may be two years away, some prospective contenders have been getting a bit of media attention

While the 2016 presidential election may be two years away, some prospective contenders have been getting a bit of media attention

By Sarah Dutton, Jennifer De Pinto, Anthony Salvanto and Fred Backus

While the 2016 presidential election may be two years away, some prospective contenders have been getting a bit of media attention. The latest CBS News/New York Times Poll asked the public whether they would like to see some of these figures, as well as other party leaders, run for president in 2016.

From a list of five high profile Republican Party leaders, former Florida Gov. Jeb Bush and Kentucky Sen. Rand Paul capture the most interest among self-identified Republicans; 41 percent of Republicans say they would like to see Bush run (27 percent say no to a Bush bid) while 39 percent say yes to a Paul candidacy (21 percent say no).

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Republicans are less enthusiastic about New Jersey Gov. Chris Christie: more say they would not like him to run for president (41 percent) than say they would (31 percent). More Republicans would like to see Sens. Marco Rubio (32 percent yes, 14 percent no) and Ted Cruz (24 percent yes, 15 percent no) run for president than not, but most don't know enough about these two politicians to say.

The Democrats

On the Democratic side, former Secretary of State Hillary Clinton is the most well-known of the political leaders measured in this poll, and most would like to see her enter the 2016 race. Eighty-two percent of Democrats would like to see Hillary Clinton run, while just 13 percent would not and 5 percent don't know enough about her to say. Vice President Joe Biden is also well-known, though Democrats are divided as to whether or not they'd like to see him make a third run for the presidency. Forty-two percent would like to see him run, but 39 percent would not.

Most Democrats don't know enough about Massachusetts Sen. Elizabeth Warren (56 percent), New York Gov. Andrew Cuomo (59 percent), or Maryland Gov. Martin O'Malley (82 percent) to say whether they'd like them to run for president.

What Do Independents Think?

In some primary contests, independents (those voters unaffiliated with a major political party) can cast a vote for a party nominee, and they are a key voting bloc in the general election as well.

Among independents, 50 percent would like to see Hillary Clinton jump in the race - the highest percentage among both the Democratic and Republican figures asked about in the poll. Thirty percent of independents would like Rand Paul to run for president (the highest among the Republican possibilities listed), but nearly as many - 29 percent-- don't want to see him run.

At this point, most independents (58 percent) are not excited about the prospect of Vice President Biden running for president, while a quarter would like to see him get in the race. Large percentages of independents don't know enough about many of the other political figures to have an opinion.

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This poll was conducted by telephone February 19-23, 2014 among a total of 1,644 adults nationwide. Data collection was conducted on behalf of CBS News by Social Science Research Solutions of Media, PA. Phone numbers were dialed from samples of both standard land-line and cell phones.

The poll included a general population sample of 1,003, along with additional interviews to yield the following sample sizes: 519 Republicans, 515 Democrats, and 610 independents. The additional interviews were obtained through callbacks to people indicating party id on a previous poll. The total sample was then weighted to party distribution targets from the general population portion of the poll.

The error due to sampling for results based on the entire sample could be plus or minus three percentage points. The margin of error for Republicans, Democrats and independents is 6 points. The error for subgroups may be higher. Interviews were conducted in English and Spanish.

This poll release conforms to the Standards of Disclosure of the National Council on Public Polls.