Washington (CNN) Sen. Lindsey Graham says he is testing the waters on a presidential run because he is sick of hearing himself complain.

"I complain a lot and also have some solutions. I'm tired of just complaining and now ready to try to lead. Whether or not there is a market for me, I won't know until I try," Graham told CNN in an interview.

Graham set up a new political organization on Thursday called "Security Through Strength," which will allow him to raise money and hire a political staff as he weighs whether to officially run for president. The South Carolina Republican said he expects to make a decision by the end of April.

Graham is a conservative, but bucks his party on big issues like immigration, where he thinks there should be a path to citizenship, and climate change, which he believes is at least in partly the result of human activity.

"Conservatism will sell to any demographic in this country as long as it's sold in a way to be inclusive and not hateful," said Graham.

He made a point of noting that he beat back several challengers from the right in a GOP primary last year for his Senate seat in South Carolina, a conservative state.

"I'm not going to run away from the idea that the President of the United States has to bring the parties together. Conservatism is an asset in terms of winning a national election, but what is needed more than conservatism or liberalism is pragmatism and somebody that can get a result. Only time will tell," said Graham.

When asked what he would bring to the table that other establishment Republicans like Jeb Bush, Mitt Romney or Chris Christie do not, Graham focused immediately on foreign policy.

"It will be about who can best protect the county, who has an alternative to Obama on foreign policy at a time when we need one," Graham said. "Ronald Reagan said that his platform was peace through strength. I've concluded that with radical Islam, peaceful coexistence is nonexistent, is a fantasy. I think I can articulate how to straighten out a screwed up world when it comes to national security."

Graham says he believes he can be competitive in Iowa, as well as New Hampshire, the second Republican contest. The next would be his home state, where he says he is confident he could win.

There is no guarantee of that, of course.

Graham won his GOP primary for the Senate in large part because he worked to keep formidable conservative opponents off the ballot. Still, South Carolina is his home turf where voters know him, and some Republicans there who relish their role as the GOP gateway to the South in the presidential process, are privately concerned that Graham getting in could effectively take that state off the map.

Graham, an Air Force reservist who is still a military lawyer, is one of the Senate's leading foreign policy hawks, so it's clear he thinks national security is his main calling card in any presidential race. But he also plans to push the desire for deal-making on the domestic front.

"I've gotta convince people that not only would I be a good commander-in-chief but I can do more than the foreign policy stuff, that I can be someone that gets both parties in a room that comes out with an outcome," said Graham.

Graham was a constant presence on the presidential campaign trail in 2000 and 2008 when his close friend, Sen. John McCain, ran for president.

McCain on Thursday called Graham his "best friend" and also recently joked that Graham, almost two decades younger than McCain, is his "illegitimate son."

"Well, I hope I get to be in his will now that I'm his illegitimate son -- which was news to me and Cindy [McCain] and everybody else," Graham joked.

But Graham then got serious, and emotional, talking about the fact that McCain has been telling anyone who will listen for months he believes Graham should throw his hat in the presidential ring.

"John is a dear friend. One of the highlights in my time in politics is him, and I know he loves me dearly," Graham said, as he tried to fight back tears. "We are truly friends, but he wouldn't say to anybody that I should be president if he didn't really mean it, and believe it."

He calls McCain's encouragement a "personal honor I will cherish," but also says that it is "not going to carry the day for me."