He didn't disappoint as he opened up a battle with Fox News anchor Megyn Kelly. Although some experts doubted that he would be able to sustain his momentum after voters were exposed to his bombastic rhetoric, his surge has continued.

Julian Zelizer

Trump remains the main attraction. No matter what he says, the Trump phenomenon only seems to grow stronger. Once again, viewers will likely be gathering around their television sets, computer screens and smart phones to see The Donald unleash his no-holds-barred attacks on the other candidates. Of equal interest is whether one of his opponents will finally be able to take him down.

But the nation has too many serious challenges for Donald Trump to be the sole issue on the debate agenda. And Republicans as a political party are confronting too many big questions for their candidates to spend the night in a contest over who can deliver the best zingers.

In the second debate, the Republican Party, as well as the nation, would benefit from being able to see the candidates answer broader questions about major issues that have emerged over the past few months.

1. Will you liberalize immigration policy or follow nativist path?

The fate of the millions of undocumented immigrants living in the United States is one of the most important human rights issues of our time. While many Republicans, after seeing Mitt Romney lose the Latino vote in 2012, were hoping that the candidates could downplay the anti-immigration rhetoric. Trump foiled this strategy by unleashing some of the harshest and most inflammatory attacks we have heard to date.

"When Mexico sends its people," he said, "they're not sending their best. They're not sending you. They're sending people that have lots of problems, and they're bringing those problems with us. They're bringing drugs. They're bringing crime. They're rapists."

Republicans have been having a civil war about immigration for over a decade. The champions of a liberalized immigration policy, who have included former president George W. Bush, keep losing out to the more conservative elements of the party.

The candidates should be pressed to make clear where each of them stands on allowing undocumented immigrants a path to citizenship. If some Republicans, like Jeb Bush or Marco Rubio, want to change the tone of their party, this is an opportunity for them to say unequivocally what they would do as president.

2. How will you make middle class more secure?

Republicans have seized on the populist moment. Trump, Scott Walker, John Kasich and others have all promised to help the "average" Americans who have been left behind in recent years. They have railed against big interests, warning that most families are struggling to make ends meet. The halting nature of the economic recovery has been one of the principal factors they've cited to question the recovery that has taken place in the last several years of President Barack Obama's administration.

The problem is that the candidates have not said much about exactly how they would actually help the middle class. Many of their stances -- going after unions[what does that mean?] or opposing the minimum wage -- would actually reduce the number of middle-class wage earning positions.

While Jeb Bush has proposed a tax plan that provides cuts to a wide range of Americans and would close some regressive loopholes, the overall impact of the plan, as The New York Times noted, would benefit the rich. Platitudes that the free market will simply do better under their leadership are not enough. Each candidate should be required to put forth one specific measure that they would push for as president that would have a positive impact on middle class family budgets.

3. Can Republicans govern?

This is the question that looms over the entire Republican Party. For all the problems that Democrats have faced with the fluctuating approval ratings of President Obama, the GOP's name brand has greatly suffered as a result of the obstructionist tactics of Republicans on Capitol Hill.

The inability to move forward on key policy issues, including even passing the regular appropriations, has greatly damaged the approval ratings of the GOP. When most Americans are asked about their positions on the party, the image that comes to mind are radical legislators on the Hill who have no interest in making things work.

The candidates should be asked about how they would address some of these problems and whether they have been comfortable with the kinds of tactics employed by congressional Republicans, including Texas Sen. Ted Cruz. As Congress enters into yet another high-stakes showdown over the budget, they should be asked more about how they would resolve these differences with the Democrats.

Cheap talk about bringing a more civil tone to Washington should not be taken seriously. We have heard that before. Rather, the candidates need to offer some clear road map about how they would try to govern in a polarized system.

4. How will you repair the political process?

This is a related question that deserves attention. Everyone agrees that Washington is broken. Money corrupts decision-making, lobbyists have too much influence on Capitol Hill and issue-based interest groups push presidents, senators and representatives away from compromise. As part of the populist fervor sweeping the campaign trail the political establishment has become enemy number one.

On the Democratic side, there has been a considerable amount of discussion about the need for campaign finance reform. Sen. Bernie Sanders has made this a centerpiece of his criticism about how democracy works. Hillary Clinton recently put forth her proposal for campaign finance reform. The questioners need to ask the candidates how they would repair the political process.

5. What's an alternative to the Iran deal?

Republicans have come down hard on the nuclear deal with Iran. They have employed some tough rhetoric about the administration, warning that the nuclear deal with result in a dangerous adversary being able to produce a nuclear weapon. According to former Vice President Dick Cheney, the deal is "madness" that will allow Iran to "launch a nuclear attack on the U.S. homeland."

Many Republicans have argued that continuing with economic sanctions, even as the rest of the world abandoned them, would have an impact. Some, like Lindsey Graham and Marco Rubio, have also brandished the sword with the clear implication that military strikes remain the best option.

Candidates should be asked to spell out how, in the absence of a deal with Iran, they propose containing the nuclear threat given there would not be much verification on the ground about what Iran is doing. The candidates need to offer voters a better alternative if they want to be compelling on Election Day.

6. How will you balance counterterrorism and civil liberties?

One area where Republicans have the potential to appeal to younger voters is civil liberties. The libertarian element of the party, best embodied by Sen. Rand Paul, has been extremely critical of the authority given to the National Security Agency since 9/11 to conduct surveillance into its citizens.

Although the furor over the Edward Snowden revelations has subsided, many voters still would like politicians to figure out a better way to keep the nation safe without totally abandoning the protections historically afforded to U.S. citizens.

But the path toward this outcome remains maddeningly vague. The issue was back in the news last week when a U.S. District Judge, Richard Leon, announced that he wanted to expedite a lawsuit that aims to end the NSA data collection program on phone calls.

The nation needs a sound long-term plan for dealing with the genuine needs for sweeping surveillance and the importance of maintaining civil liberties in our democratic society. It would be useful to hear Paul and others explain what the next steps in this process should be.

If Republicans answer some of these questions, their primary process might start to look a little more solid. Rather than a World Wrestling Entertainment steel-cage match, the nation could be treated to a more serious and robust discussion about public policy.

Join us on Facebook.com/CNNOpinion.
Read CNNOpinion's Flipboard magazine.