Texas Sen. Ted Cruz is just 4 percentage points behind Republican presidential front-runner Donald Trump in a new national poll released Tuesday by Quinnipiac University.

Trump leads the pack with 28 percent support, a one point increase from the university's last poll. Cruz, however, surged eight points to 24 percent.

While Trump's national lead has reached new heights in recent polls, Cruz has far surpassed the real estate mogul in the key state of Iowa. RealClearPolitics' average of polling data shows Cruz leading with 30.2 percent compared to Trump's 26.2 percent. Cruz also recently tied Trump in his stronghold of South Carolina, according to Capital New York.

In the Quinnipiac poll, Florida Sen. Marco Rubio placed third with 12 percent support, followed by retired neurosurgeon Ben Carson with 10 percent, New Jersey Gov. Chris Christie with 6 percent and former Florida Gov. Jeb Bush with 4 percent. Kentucky Sen. Rand Paul and businesswoman Carly Fiorina tied with 2 percent each, and 8 percent were undecided. Most respondents, 58 percent, said they may decide to support a different candidate before casting ballots in their state's primary.

Cruz was the top pick among those describing themselves as members of the tea party, with 38 percent, compared to 27 percent for Trump. White, born-again evangelical Christians also favored Cruz over Trump, 33 percent to 22 percent, as did very conservative supporters, 38 percent to 27 percent, noted Politico.

Among men, though, Trump was still the favorite, garnering 30 percent support to Cruz's 29 percent. Those with college degrees preferred Cruz to Trump, 24 percent to 21 percent.

Of all the Republican voters, 40 percent said Cruz won the GOP debate on Dec. 15, while only 20 percent thought Trump performed the best.

On the Democratic side, Hillary Clinton continues to lead Bernie Sanders by a wide margin, winning 61 percent of the vote to Sanders' 30 percent.

When Clinton was matched up against Trump in a hypothetical head-to-head, the former secretary of state beat him by 7 points and Sanders beat him by 13 points. Other Republicans fared much better than Trump, with Cruz tying Clinton at 44 percent and Rubio only losing to Clinton by one point.

Quinnipiac also asked respondents whether they would be embarrassed or proud to have Trump or Clinton as president. Fifty percent said they would be embarrassed to have Trump as their commander in chief, 23 percent said they would be proud and 24 percent said they would not feel embarrassed or proud. Voters were more split on Clinton, with 35 percent saying they would be embarrassed, 33 percent proud and 29 percent neither.

The telephone poll was conducted after the last Republican debate, from Dec. 16-20, among 1,140 registered voters and has a margin of error of plus or minus 2.9 percentage points. For the 508 Republicans polled, the margin of error is plus or minus 4.4 percentage points, and for the 462 Democrats, the margin of error is 4.6 percentage points.