Haley told a national audience Tuesday night that Republicans have not been as inclusive as they should be, specifically pointing to Donald Trump's comments about banning Muslim emigrants to the United States.
Those comments triggered a conservative backlash, including from Trump himself, who noted her prospects for being tapped to be his vice presidential candidate are not very high.
"Well considering I'm leading in the polls by a lot, I wouldn't say she's off to a good start" to be his vice presidential candidate, Trump said Wednesday on Fox News. "Whoever I pick is also going to be very strong on illegal immigration."
"She's very weak on illegal immigration," he said. "I feel very strongly about immigration. She doesn't."
Haley stressed Wednesday that Trump is a "friend" but encouraged him not to "take it personally."
"Just because you disagree with somebody doesn't mean you're not a friend," Haley told reporters. "When I say it about my other friends that are running for president, they don't throw stones."
"This is just something that we learned in South Carolina that I'm passing along," said Haley. "Take it if you want, don't take it if you don't."
Haley stressed that she wrote the speech herself and without guidance from the Republican congressional leadership who tapped her to give the address. Her speech was at times critical of Republicans writ large, not just Trump.
"We have to really look at the responsibility we have and what we want to do to keep this country the greatest, freest country in this world and that just means making sure everyone feels welcome," the Republican governor told CNN's Don Lemon on "New Day."
"We see Republicans who are not always being responsible with their words in terms of extending our tent, making sure that people who abide by our laws and abide by our traditions feels accepted in this country," she added.
Republicans could do a better job of working Democrats if politicians checked their egos at the door, the governor said.
"It takes everyone to get their egos out the room and really sit down and say, 'OK, How are we going to get to a solution?' And that's something we're not seeing in D.C. right now," she said.
"This is something where both parties need to realize there are no saints here but there are opportunities where we can say, 'Let's right the ship and start moving forward'," she added.
But Haley also blamed Obama for dividing the nation.
"President Obama has been very divisive, We've seen him divide the country in a lot of ways." she said. "We have to make sure we're not a part of that. We need to look in the mirror."
"And say, 'OK, we're going to be positive role in this,'" Haley added of the GOP. "We're going to move forward and get out of all of the political rhetoric. If we're really going to do something, we need to show actions not words."
Lemon asked Haley if statements in her speech about "the angriest voices" were attacks on Trump.
"Yes, partially to Donald Trump but partially to a lot of other people reminding them we get more done when we listen and find out where someone else is coming from and put ourselves in their shoes to try and figure out where we can find common ground," she said.