Tea-party activist Sal Russo offered an eye-opening remark this week. He said: "Conservatives should be leaders in the immigration-reform movement." Then tax-reform activist Grover Norquist organized a media conference call in which he reinforced his support of immigration reform. American Conservative Union chairman Al Cardenas joined in that call, as did Robert Gittelson, president of Conservatives for Comprehensive Immigration Reform.

In recent days, support for legal status for undocumented immigrants was also voiced by Sen. Rand Paul, Texas Gov. Rick Perry, and former Florida Gov. Jeb Bush, all GOP presidential contenders.

House Speaker John Boehner has denied making any clear commitment to the White House to overhaul immigration, distrustful that President Barack Obama will enforce a deal combining border security with legalization and possibly citizenship. But Boehner has laid down clear immigration-reform principles that have proven widely popular.

So the political tide among conservatives and Republicans may be turning in favor of immigration reform. As a longtime supporter of reform who believes that immigration is a pro-growth issue—I am delighted to see these developments.

If the GOP is to recapture the Senate come November and move on to retake the presidency in 2016, it must have a strong pro-growth message. Jobs and the economy are going to be key issues. Tax reform, regulatory rollbacks and a rewriting of Obamacare that ends the mandates and provides real health-care freedom to choose are vital points.

But so is the immigration issue.

Not only because it is pro-growth, but because the Republican Party must return to its big tent roots. It must follow the lead of Ronald Reagan and Jack Kemp. It must reach out to Latinos, African-Americans, young people and women. A conservative Catholic like myself can work inside the same tent as my Log Cabin Republican friends.

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In doing so, the GOP can maintain its core conservative principles of economic growth, limited government and military strength. As Reagan taught us, strength at home in the domestic economy is vital to strength abroad in national security. That must not change. Nor should the GOP's longtime support for defending the life of the unborn.

But the GOP will not be successful unless it actively reaches out to groups that have recently deserted it. It must show independents and disaffected Democrats that the Republican Party is open for business, ready to spread its wings to attract greater support.

Immigration reform is a crucial symbol in the GOP reach-out effort. It will create new trust in a party that can govern for all.

All the recent polls say immigration reform is popular. A survey by the Partnership for a New American Economy shows that around 70 percent of Republicans who identify with the tea-party movement support immigration reform. They back the idea of undocumented immigrants obtaining either legalization or a path to citizenship. And 76 percent of surveyed Republicans support improved border security and letting immigrants remain in the U.S., while 69 percent say they would also support a candidate who backs broad reform.

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Other polls from Gallup, CNN/ORC, Fox News, and CBS News agree. In fact, the Fox News poll indicates that more than two-thirds of Americans support a pathway to citizenship and reject mass deportation.

As Russo, co-founder of the Tea Party Express, put it, "We need to make the 11 million people who are here illegally obey the law, pay taxes and come out of the shadows. We have to get them right by the law in exchange for legal status, but not unbridled amnesty. This should include penalties, background checks to root out criminals and the requirement that they learn English, understand the Constitution and be committed to our basic freedoms. We must ensure there is no special pathway to citizenship that puts them in front of people who waited in line."

There's no reason why this can't be done.

Republican economist and former Congressional budget Office Director Douglas Holtz-Eakin argues that more rapid overall population growth will generate more rapid GDP growth and increased productivity. He notes that labor-force participation rates are higher among the foreign-born, and suggests that real GDP growth could rise from 3 percent to 3.9 percent on average annually over the first 10 post-reform years, reducing the budget deficit by nearly $3 trillion.

What's more, immigration restrictionists are wrong to cite a CBO estimate that increased immigration will cost jobs. Yes, there could be a minor 0.1 percent transitory uptick in the unemployment rate. Meaningless. Over the longer term, the CBO agrees with Holtz-Eakin's conclusions.

Pro-growth immigration reform will strengthen the shaky economy. Politically it will help the shaky GOP. And on the road to capturing all three houses in Washington in 2016, it will send a new message about a new Republican Party.

—By CNBC's Larry Kudlow; Follow him on Twitter @larry_kudlow