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

Immediately after Saturday night's Republican debate, CBS News interviewed a nationally representative sample of debate watchers assembled by GfK's Knowledge Panel who identified themselves as Republicans or independents.

Thirty-two percent of these debate watchers say Marco Rubio won the debate, beating out Donald Trump (24 percent) and John Kasich (19 percent), who are ranked second and third, respectively. Further down on the list are Ted Cruz (12 percent), Ben Carson (8 percent), and Jeb Bush (5 percent).

Marco Rubio is the clear favorite among Republicans, while independents are largely divided between Trump, Kasich, and Rubio.

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Donald Trump has been leading national polls for months, and he is seen by Republican and independent debate watchers as the most likely -- with 42 percent -- of the six candidates to win in November should he get the nomination. But Marco Rubio comes in second (22 percent), beating out Ted Cruz (14 percent) by eight points.

In light of the breaking news about the death of Supreme Court Justice Antonin Scalia, the candidates were asked during the debate about presidential appointments to the Supreme Court. No candidate last night seemed to have a clear advantage as to who is most trusted to appoint justices to the Supreme Court.

Donald Trump is the clear leader on values. Twenty-seven percent of Republicans and independents who watched the debate pick Trump as the candidate who most shares their values, with Ben Carson and Marco Rubio tied for second place, each with 16 percent. Rubio does better than Kasich among Republicans, while Kasich does better than Rubio among independents.

But when it comes to the candidate who is best prepared to be President, Republicans and independent debate watchers choose John Kasich first (22 percent), just edging out Donald Trump (20 percent) by two points.

Still, Donald Trump enjoys a strong leading position on all the issues measured in this poll: the economy, immigration, terrorism, and bringing needed change. Rubio comes in second - ahead of Cruz - on immigration. Kasich comes in second on the economy and jobs.

This CBS News poll was conducted online using GfK's web-enabled KnowledgePanel®, a probability-based panel designed to be representative of the U.S. population. The poll was conducted among a nationwide random sample of 601 voters who identified themselves as Republican or independent who watched the debate.

GfK's KnowledgePanel®'s participants are initially chosen scientifically by a random selection of telephone numbers and residential addresses. Persons in selected households are then invited by telephone or by mail to participate in the web-enabled KnowledgePanel®. For those who agree to participate, but do not already have Internet access, GfK provides at no cost a device to connect to the internet.

This is a scientifically representative poll of these voters' reaction to the debate. The margin of sampling error could be plus or minus 4.5 percentage points for results based on the entire sample.