Although he said tough immigration stances may help Republicans in some states, he worried that in the long-term, it will cost Republicans votes with Hispanics, a rapidly growing segment of the population.

"We've got to have a better tone going forward over the long haul for sure," Bush said. "You can't ask people to join your cause and then send a signal that you're really not wanted. It just doesn't work."

Bush emphasized that he believes it is important to secure the border and block illegal immigration. But he argued that allowing more young people to work legally in the country would boost economic growth.

"We need young aspirational people to come to our country so that we can grow over a sustained period of time at a high rate," Bush said.

Bush supports the Dream Act, which would give legal status to some young people brought to the country illegally. 

Polls show presumptive GOP nominee Mitt Rommey trailing Obama among Hispanics by a wide margin. An  NBC News-Wall Street Journal-Telemundo poll released last week showed Obama topping Romney by 63 percent to 28 among the key demographic.

In the 2008 election, Obama took 67 percent to GOP nominee Sen. John McCainJohn Sidney McCainOn The Money: GOP digs in on defending Trump tax cuts | Democrats bullish on raising minimum wage | Financial sector braces for Biden's consumer bureau pick No. 2 Senate Democrat says minimum wage can be increased with simple majority vote State-level Republicans wracked by division after Trump's loss MORE’s (Ariz.) 32. 

The Romney campaign told The Hill this week it needs to take 38 percent of the Hispanic vote to defeat President Obama.