Potential GOP rivals react to Ted Cruz's announcement

The official Republican presidential campaign is still a one-man race. Texas Sen. Ted Cruz became the first declared candidate on Monday, but his potential rivals are not rushing to join him.

If Cruz got an advantage by jumping in first, his would-be opponents certainly won't admit it, reports CBS News correspondent Nancy Cordes. One even said point blank he's better positioned to win, even as he claimed he's still making up his mind.

"We're pretty close to a decision," Kentucky Sen. Rand Paul said.

Paul argued if he runs, he can beat Hillary Clinton and Cruz can't.

"Ted Cruz is a conservative, but it also goes to winnability," Paul said.

New Jersey Gov. Chris Christie downplayed Cruz's influence, during his monthly "Ask the Governor" radio show.

"Ted Cruz formally announced today he was running for the nomination, others are expected to do so, is that a factor in your decision at all?" the radio host asked.

"No," Christie responded.

Cruz announced his candidacy Monday at Christian Liberty University in Lynchburg, Virginia.

He said he would end Obamacare and abolish the IRS, replacing it with a simple flat income tax.

Later, on Fox News, he said the Obama White House has projected an image of a weakness to the world.

"The consistent pattern of the Obama-Clinton foreign policy has been abandoning our friends and allies, whether it is Israel, whether it is the U.K., whether it is Canada, and coddling and appeasing our enemies," Cruz said.

Announcing early also means becoming a target for late night jokes.

"He was born in Canada, his father fled to the United States from Cuba, yet Ted Cruz is against immigration. Is that odd?" "Late Show" host David Letterman asked.

As Republicans jockeyed for position, Hillary Clinton sought to rebound from her personal email controversy.

"I am all about new beginnings: a new grandchild, a new new hairstyle, a new email account, why not a new relationship with the press," Clinton said.