Has Karl Rove gone soft? Or are House Republicans who defy President Bush’s wishes for comprehensive immigration reform about to get some party discipline? If Republicans can’t achieve some results on the immigration issue before the election, will it threaten the GOP majority?

That’s the most important set of questions facing the Republican Party these days.

Polls clearly and consistently show that large percentages of Americans believe illegal immigration is a major issue that needs legislative attention. These same polls demonstrate that large majorities of Americans support comprehensive reform that includes some sort of path to citizenship for illegals, in addition to improved border security and employer sanctions. In short, the public generally embraces the Bush approach to the issue.

While most Republicans in the Senate seem to understand these realities, most of their colleagues in the House seem intent on thumbing their noses at Bush and the party’s best interests. Instead of accepting the leadership of their president, they have decided to parade across the country holding inflammatory hearings that they believe support their positions.

It’s not just the immigration issue that is affected by lack of party discipline. The excessive spending that typifies today’s congressional Republican may also stem from inadequate discipline.

A recent paper, “Party Discipline and Pork Barrel Politics,” by two Ivy League professors, Gene M. Grossman of Princeton University and Elhanan Helpman of Harvard University, develops a model of congressional behavior that explains the fiscal decisions of members. The paper concludes, in very polite language, that “when party discipline is lax, spending on public goods will exceed the socially efficient level.”

The paper even provides insight on the type of rhetoric that we see in abundance on the immigration issue: “Political rhetoric will be shrill when party discipline is lax.”

Party discipline doesn’t have to involve ugly, public displays of dissatisfaction with members’ actions. Discipline can be imposed in many quiet ways. Access to campaign funding and information can be limited. Special perks and privileges of access to White House and party events can be curtailed. Future committee chairmanships and prized office space should hang in the balance.

Consultants themselves can help the cause. Recently, I resigned as pollster for a member who virulently and repeatedly attacked any and all Republicans who disagreed with his narrow, hard-line approach to the immigration issue. I am sure this member quickly found a replacement, but if enough consultants respected the president’s wishes on this very important issue it could make a difference.

I am not suggesting that every member and consultant has to always toe the party line as articulated by a president or governor. In fact, in the past I have supported candidates and issue positions that don’t conform to party leadership preferences. I am doing so now. In Florida, I am helping a distinguished state Senate candidate seeking reelection that is being opposed by Gov. Jeb Bush (R) because the senator didn’t support one of the governor’s education initiatives. On principle, I am helping the incumbent, yet I still accept and even respect the fact that Gov. Bush is trying to impose some party discipline as he sees fit.

The Wall Street Journal is about the only major media outlet pushing hard and consistently for the president’s plan. But anti-immigrant zealots who bring more heat more regularly outgun the Journal.

An enforcer is needed to get a comprehensive bill. Sounds like a job for Karl Rove to me.

Hill is director of Hill Research Consultants, a Texas-based firm that has polled for GOP candidates and causes since 1988.