U.S. Republican front-runner Donald Trump expressed confidence on Saturday that he could push back attempts by his rivals to knock him off his top perch, saying he could stand in New York's Fifth Avenue "and shoot somebody" and not lose voters.

Trump and Texas Senator Ted Cruz, Trump's chief obstacle to a victory in Iowa's Feb. 1 caucuses, held competing rallies across the state while in New Hampshire, other candidates battled for votes in that state's Feb. 9 first-in-the-nation primary.

Trump, the New York billionaire and former reality TV star who has been virtually impervious to attacks from his opponents, pushed the limits of his political rhetoric again in Sioux Center, Iowa.

"I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn't lose any voters," he said.

Cruz picked up the endorsement of conservative firebrand Glenn Beck, a counterweight of sorts to Trump's endorsement by 2008 vice presidential nominee Sarah Palin.

Beck quickly went on the attack during a 45-minute speech at the Cruz event in Ankeny.

"If Donald Trump wins (Iowa), it's going to be a snowball to hell," Beck said.

Their comments came on the day The Des Moines Register, Iowa's largest and most influential newspaper, was to announce who it is endorsing for both the Republican race for a presidential nominee but also the Democratic battle between Hillary Clinton, Bernie Sanders and Martin O'Malley.

The potential for more chaos in what has been a turbulent race on both the Republican and Democratic sides emerged on Saturday with the news that former New York Mayor Michael Bloomberg might launch an independent run for president.

A source said part of Bloomberg's concern was the problems that Clinton is having in defeating Sanders.

Trump has been a difficult target for criticism from his rivals because not all of his supporters are conservatives and many are most interested in his projection of strength, not where he stands on a particular issue.

The latest Reuters-Ipsos tracking poll had Trump pulling in 40.6 percent support of Republican voters nationally. A CNN/ORC poll has Trump up in Iowa with 37 percent to 26 percent for Cruz, who has led in some other Iowa polls.

At a First In The Nation forum for candidates in Nashua, New Hampshire, former Florida Governor Jeb Bush was notably withering in his criticism of Trump, calling him a fake conservative with a liberal past and a tendency to insult people.

He reminded voters of Trump's dismissal of Senator John McCain as not a hero because he got captured during the Vietnam War. McCain spent 5-1/2 years as a prisoner of war. He was a two-time winner of the New Hampshire primary and the 2012 Republican presidential nominee.

"It is not strong to insult women. It is not a sign of strength when you insult Hispanics. It is not a sign of strength when you say that a POW was a loser because they got caught. John McCain is a hero. It is not a sign of strength disparaging the disabled in this country. It is not. It is a sign of deep insecurity and weakness," Bush said.