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

Thirty-five percent of Republican primary voters support Trump, up 13 points since October, and his highest level of support in CBS News polling. Ted Cruz (16 percent) has moved into second place, while Ben Carson, who led the October poll, has dropped to third.

Marco Rubio is in fourth place with 9 percent. Jeb Bush is getting the backing of just 3 percent of Republican primary voters nationwide, his lowest percentage to date in CBS News polling. Carly Fiorina's support has also dropped; she is at just 1 percent now.

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Most of the interviews for this poll were conducted before Trump made statements concerning a ban on Muslims entering the United States.

Trump voters continue to be more firm in their support. Fifty-one percent of his backers say their minds are made up about him, compared to just a quarter of voters who support a candidate other than Trump.

The Candidate on the Issues

As terrorism emerges as the public's top issue and concerns about an attack are on the rise, Republican voters see Trump as best able to handle that issue. He is also seen as stronger than his opponents on the economy.

More Republican primary voters are very confident (40 percent) in Trump's ability to handle the threat of terrorism than any other candidate asked about in the poll. Cruz also does well on this issue. Trump has a clear advantage on the economy - 51 percent are very confident he would make the right economic decisions, far more than his Republican opponents.

Republican primary voters express the lowest level of confidence in Bush on both these issues.

Voters' Views of the Republican Field

While the nominating contests have yet to get underway, Republican primary voters now expect Trump to be the party's nominee. Fifty-one percent think he'll win the nomination, far ahead of any other candidate. A large majority of his supporters think Trump will be the nominee, but even those not currently backing Trump pick him as the expected nominee.

Trump appears to have tapped into public anger toward Washington. About a third (31 percent) of Americans are angry about how things are going in Washington, but that number rises to 44 percent of Republican primary voters, and Trump supporters (52 percent) are more likely to say they're angry at Washington than those supporting other candidates (38 percent).

No candidate stands out as a clear second choice among Republican primary voters, but 26 percent of Trump supporters say Cruz would be their second choice.

Trump is a polarizing figure. In this fractured field, he also tops the list as the candidate Republicans would be most dissatisfied with as the party's nominee, followed closely by Bush.

Candidate Support

Trump leads among both men and women. He has more than a 20 point lead among non-college graduates (and a smaller lead among those with a college degree).

But Cruz has made inroads with evangelicals. Carson led with this group in October, but now Cruz and Trump are running neck and neck among them, the two candidates are also close among very conservative Republicans.

Candidate Qualities

Most Republican primary voters think Trump and Cruz have presented specifics about how they would accomplish their goals if they become President. About half say this about Rubio too, while voters are more closely divided on whether Carson has presented specifics. Republicans are more inclined to say Bush has not offered specifics than say he has.

Trump continues to be viewed as someone who says what is on his mind. Three in four Republican primary voters think he says what he believes. Majorities say this about Carson and Cruz as well. Republican voters are also inclined to say that Rubio says what he believes, but a majority thinks Bush mostly says what people want to hear.

What are Republican Primary Voters Looking For in a Nominee?

Republican primary voters pick strong leadership (42 percent) as the most important quality in their choice of a nominee, followed by honesty (30 percent). Further behind are caring about people like them (12 percent), having the right experience (8 percent) , or being able to win the general election in November (6 percent).

Trump dominates the field among those primary voters who value leadership. Among those who say honesty is the most important quality, the top tier candidates run about even.

By a large margin, Republican primary voters continue to say that positions on the issues matter more to them than electability.

Trump's strong position in this poll reflects some Republican primary voters' continued desire for a candidate from outside the political world. Forty-three percent prefer a candidate who has experience in business or the private sector, while 13 percent want a candidate with experience mostly in politics. Forty-two percent say it doesn't matter to them.

Looking ahead, most Republican primary voters want a candidate who will compromise with Democrats in Congress in order to get things done, but 38 percent would have rather have someone who will stick to their positions on the issues even if it means not getting as much done. In a poll conducted last month, Democratic primary voters were more likely to want a nominee who would compromise.

Voter Enthusiasm

About two-thirds of registered voters nationwide are at least somewhat enthusiastic about voting in 2016, but there is a partisan enthusiasm gap: Republican primary voters are more enthusiastic about voting than those who plan to vote in a Democratic primary.

Looking Past November 2016

While the general election is nearly a year away, the poll asked registered voters nationwide how they would feel if each of the party's current front runners became president. Neither is met with a lot of enthusiasm, but there is somewhat more anxiety about a Trump presidency (64 percent) than a Clinton one (57 percent).

Perhaps not surprisingly, views differ greatly by political party. Seventy-six percent of Democrats would be either excited or optimistic if Hillary Clinton became president, while most would be skeptical about the prospect of a Donald Trump presidency, including 63 percent who say they would be scared.

Republican voters hold contrasting views: Sixty-six percent would be excited or optimistic if Donald Trump was elected president, but most would be concerned or scared if Clinton won the White House.

Independent voters, a key voting bloc, are not especially enthusiastic about either a Clinton or a Trump presidency, but more are concerned or scared about Trump (67 percent) than they are about Clinton (59 percent).

This poll was conducted by telephone December 4-8, 2015 among a random sample of 1,275 adults nationwide, including 1,053 registered voters. Data collection was conducted on behalf of CBS News and the New York Times by SSRS of Media, PA. Phone numbers were dialed from samples of both standard land-line and cell phones.

The poll employed a random digit dial methodology. For the landline sample, a respondent was randomly selected from all adults in the household. For the cell sample, interviews were conducted with the person who answered the phone.

Interviews were conducted in English and Spanish using live interviewers.

The data have been weighted to reflect U.S. Census figures on demographic variables.

The error due to sampling for results based on the entire sample could be plus or minus three percentage points. The error for subgroups may be higher and is available by request. The margin of error includes the effects of standard weighting procedures which enlarge sampling error slightly.

The margin of error for the sample of 431 Republican primary voters is 6 percentage points.

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