Washington (CNN)Former Florida Gov. Jeb Bush's surprise announcement that he'll "actively explore" a presidential bid Tuesday morning did little to dissuade his potential Republican opponents from the race. 

Following the news, South Carolina Sen. Lindsey Graham, who might make a White House bid, offered the clearest pitch yet for his own candidacy. 

"I think I have a unique ability to deal with the threats we face at home and abroad and the challenges here, which is finally getting the government to work and dealing with a dangerous world," he told reporters on Capitol Hill. 

He said to "stay tuned" for his plans. 

"I think there are a lot of people in the donor class who are looking for multiple voices, including Jeb's, and competition is a good thing," Graham said, adding, "He's got a lot to offer the Republican Party and the country." 

Kentucky Sen. Rand Paul was upbeat about the governor's announcement. 

"I think we're a big tent — we can use moderates, conservatives, libertarians — we need 'em all," he told reporters. "I think the more the merrier — the public will determine" whether Bush could win. 

And Florida Sen. Marco Rubio's spokesman, Alex Conant, said while Rubio has "a lot of respect" for Bush and thinks he'd make "a formidable candidate," Bush's decision has no bearing on his own. 

"Marco's decision on whether to run for president or re-election will be based on where he can best achieve his agenda to restore the American Dream — not on who else might be running," Conant said. 
Who is Rand Paul?
Kentucky Sen.