Simi Valley, California (CNN) -- Rudy Giuliani's still the front runner in the polls as the Republican presidential hopefuls tangle for the first time tonight at the Ronald Reagan Presidential Library. But the former two-term New York mayor's lead is shrinking a bit. In CNN's "poll of polls," an average of the national polls the past month, Giuliani's lead over Arizona Senator John McCain is 12 points -- down from the 14 points lead Giuliani had in March.

Former Massachusetts Governor Mitt Romney and former Tennessee Senator Fred Thompsonare neck-and-neck for in the battle for third place. That's pretty impressive for Thompson, who's not even a candidate yet. He's flirting with the idea of jumping into the race for the White House.

McCain was the early front-runner in the polls, but Giuliani, after putting his hat in the ring in late January, soon took over from McCain. He also pulled ahead of McCain in the battle for campaign cash.

But the race is now tightening up in the national polls and McCain's now on top in new polls this week in three crucial primary states, Iowa, New Hampshire and South Carolina.

According to CNN Polling Director Keating Holland, "the GOP race is tightening mostly because Giuliani's losing support. McCain is the beneficiary but with the exception of New Hampshire, it looks like McCain is holding steady or even losing some support himself."

Why is Giuliani dropping? Holland says that "maybe it's just a case of front-runner fatigue. Front runners are always most at danger of losing casual support."