Donald Trump remains the Republican frontrunner, but half of American voters say they would feel "embarrassed" to have Trump as the country's president, a new Quinnipiac poll finds.

The survey shows that 28 percent of Republicans back Trump as the party's nominee, with Sen. Ted Cruz of Texas close behind at 24 percent. Florida Sen. Marco Rubio comes in third at 12 percent, while Dr. Ben Carson captures 10 percent support.

But asked whether they would be proud or embarrassed if Trump is elected, fully 50 percent of all registered voters suggested that they would feel ashamed. That includes 20 percent of Republicans, 47 percent of independents and 82 percent of Democrats.

Just 23 percent of voters responded that they would feel proud to have Trump as the country's leader.

When the same question was asked about Democratic frontrunner Hillary Clinton, 33 percent said they would feel proud, 35 percent said they would feel embarrassed, and 29 percent said that neither sentiment would apply.

The Quinnipiac poll was conducted December 16-20 and has a margin of error for all registered voters of +/- 2.9 percentage points.