Who would Americans like to see on the campaign trail in 2016?

The list of potential candidates for the presidency in 2016 is immense. The list of declared contenders, though, is nonexistent.

If the latest CBS News poll is any indication, Americans would like to see a number of potential candidates take the plunge -- but not all of them.

Republicans have a particularly broad field of prospective candidates, and it's seemingly growing by the day: Just last week, the 2012 GOP nominee, former Massachusetts Gov. Mitt Romney, told a room of donors in New York City that he's seriously entertaining a 2016 bid.

Fifty-nine percent of Republicans would like to see Romney jump into the 2016 race, while only 26 percent believe he should stay out, according to the CBS News poll.

Fifty percent of Republicans would like to see former Florida Gov. Jeb Bush on the campaign trail as well, while 27 percent disagree. If both Romney and Bush run, analysts expect them to wage a competitive battle for the allegiance of the Republican establishment.

Another potential candidate viewed favorably by the GOP establishment, New Jersey Gov. Chris Christie, is sought less eagerly by Republicans. Only 29 percent say they'd like to see Christie launch a bid, while 44 percent say otherwise. (Only former Alaska Gov. Sarah Palin's numbers are more underwater: 30 percent of Republicans say they'd like to see her run, but 59 percent disagree.)

Former Arkansas Gov. Mike Huckabee posts a respectable showing, with 40 percent of Republicans urging him to get in, and 29 percent urging him to stay out.

A trio of Republican senators who have stoked the enthusiasm of the grassroots have mixed numbers. Twenty-seven percent of Republicans would like Kentucky Sen. Rand Paul to mount a bid, but 34 percent disagree. Twenty-six percent would like Florida Sen. Marco Rubio to run, while 19 percent would not. Twenty-one percent want Texas Sen. Ted Cruz to run, while 25 percent want him to not run.

Republicans are similarly lukewarm on some of the party's governors. Twenty-one percent want Gov. Rick Perry, R-Texas, to run, but 32 percent disagree. Fourteen percent want Gov. Bobby Jindal, R-Louisiana, to run, but 20 percent disagree. Wisconsin's Scott Walker fares better, however: 22 percent want him to run, while 12 percent don't.

Finally, 19 percent of Republicans would like to see former Pennsylvania Sen. Rick Santorum run, while 29 percent would not. And 21 percent would like to see a campaign by Dr. Ben Carson, a retired neurosurgeon and conservative activist, while 17 percent disagree.

Republicans, by a 61 to 35 percent margin, believe it's more important to have a nominee who agrees with them on the issues than a nominee who can win the general election.

Democrats are similarly concerned with ideological purity: 63 percent say it's more important to have a nominee who agrees with them, while 35 percent say it's more important to pick a winner.

But the Democratic presidential field is considerably less diverse, with most of the popular anticipation coalescing around former Secretary of State Hillary Clinton.

Eighty-five percent of Democrats would like Clinton to dive in, while 11 percent want her to stay out.

Her closest competitor, Vice President Joe Biden, is sought by only 40 percent of Democrats. Thirty-eight percent want Biden to stay on the sidelines.

Twenty-three percent say Massachusetts Sen. Elizabeth Warren, a darling of liberal activists, should launch a bid, but 20 percent disagree.

Beyond those three, Democrats' excitement about their potential field is lacking. Only 16 percent want New York Gov. Andrew Cuomo to run, while 18 percent disagree. Twelve percent would like to see Vermont Sen. Bernie Sanders, an independent who caucuses with Democrats, to run, while 16 percent want Sanders to keep his day job. Three percent want former Gov. Martin O'Malley, D-Maryland, to run, but 13 percent don't. And 6 percent of voters want former Sen. Jim Webb, D-Virginia, to run, but 14 percent disagree.

Webb is the only candidate on the Democratic side who has taken even the preliminary step of forming a presidential exploratory committee.

It's worth noting that many of the names aren't widely known enough for most Americans to render a decision on whether they should run. A majority of Republicans nationwide say they do not know enough about six of the 13 Republicans in the poll to say whether they should run for president. Among Democrats nationwide, the same is true of five of the poll's seven Democrats.

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The poll, which was conducted by telephone January 9-12, surveyed 1,001 adults nationwide. The margin of error for numbers drawn from the full sample is plus or minus 3 percent, while the margin of error for results compiled from only Republicans or Democrats is plus or minus 6 percent.