Watch "Guns in America," CNN's town hall meeting with President Obama on Thursday at 8 p.m. ET

Spirit Lake, Iowa (CNN) Sen. Ted Cruz, who is working to solidify his lead in the crucial early voting state, on Wednesday accused President Barack Obama of wanting to take Americans' guns away despite his assurances otherwise.

"He's not telling the truth," Cruz said flatly during an interview with CNN aboard his campaign bus.

The GOP presidential front-runner here in Iowa, where he is in the middle of a six-day bus tour, argued that the President is focusing on the wrong problem when it comes to curbing gun violence.

"Look, he's targeting private consensual gun sales between law-abiding citizens and this is what Obama gets wrong over and over again ... he can't distinguish between what good guys and bad guys," said Cruz.

On Tuesday, President Barack Obama unveilied a series of executive actions designed to help prevent gun violence, including expanding background check requirements for private gun sales. The President will make the case for his decision, and try to convince the public more steps are needed, during an hour-long town hall on CNN Thursday night.

In addition to slamming Obama's executive actions, Cruz defended posting a picture of the President wearing military style garb on his campaign website, with the caption "Obama wants your guns."

"It is actually quite accurate. This is the most anti-gun president we've ever seen," Cruz said.

When pressed on why he doesn't take the President at his word that his goal is to protect innocent people -- children -- from gun violence, Cruz brought up one of his Senate colleagues, who is a prominent anti-gun Democrat.

"Sen. Dianne Feinstein, who said, 'if I could go to Mr. America, Ms. America, and say, hand over your guns, I want all of your guns, I would do it.' I believe Dianne when she said that. And you know what? Barack Obama is in exactly the same boat," Cruz told CNN.

Cruz cut his teeth in conservative legal circles advocating gun rights.

Cruz has a long history advocating for gun rights. In fact, he became known nationally by conservatives in part by leading a charge as Texas solicitor general to gather support from 31 states for a Supreme Court amicus brief advocating overturning a Washington gun ban.

His argument in that case, District of Columbia v. Heller, was that the right to bear arms is not a state issue, but an individual right, and a majority of Supreme Court justices agreed.

Now, Cruz is warning that a Hillary Clinton presidency would threaten that right.

"Hillary Clinton, for example, has said she will put Supreme Court justices on the court who will overturn Heller," he said.

How would Cruz curb gun violence?

The freshman Texas senator pointed to legislation he sponsored with Iowa Sen. Chuck Grassley which puts the focus on law enforcement, arguing that the Obama administration doesn't adequately prosecute felons who try to buy a firearm illegally.

Cruz pointed to 2013 as an example.

"There were 54,000 felons and fugitives who tried to illegally buy a firearm. Do you know how many of those the Obama administration prosecuted? Forty-four. Forty-four out of 54,000 were prosecuted," he said.

Cruz -- a staunch advocate of slashing most government spending -- says he would actually be willing to increase the federal budget when it comes to school safety.

Immigration flip-flop?

During CNN's debate last month, Florida Sen. Marco Rubio went after Cruz for advocating legalization for undocumented immigrants -- then shifting his position when he started to run for president. Cruz and his campaign argue the legislation was only part of a larger strategy to torpedo a bipartisan bill, co-sponsored by Rubio that would have gone further -- allowing a path to citizenship.

But Cruz is not denying changing his position on issue pertaining to legal immigration -- so called H1B visas for high-tech workers.

Many American businesses to support and even rely on high-skilled foreign workers -- and GOP pro-business interests pushed lawmakers to expand the program.

In 2013, Cruz pushed to increase the high-tech worker visas, strongly advocated by many American businesses, by some 500%.

Two months ago, as part of his campaign-trail immigration plan, Cruz called for the entire H1B program to be suspended, as he woos the more populist wing of the GOP -- those more worried about the plight of workers than their bosses.

In his interview with CNN, he admitted the change of heart -- but insisted it wasn't a politically motivated flip.

"Any rational person responds to a change in circumstances. What's changed? We've seen a whole number of employers abusing the program," he said. "No. 1, bringing in people who are not high-skilled, bringing in medium- and low-skilled (information technology) workers and then firing American workers and, adding insult to injury, forcing the American workers to train their foreign replacements."

Iowa expectations

Cruz is leading the Iowa polls and on his bus there is an air of cautious confidence. Campaign aides say their unique grassroots operation using ultra savvy technology to collect data and metrics about voters will mean victory.

But four weeks can be a lifetime in politics, and Cruz made clear he knows how precarious the catbird seat can be.

"The only way I've ever run is as an underdog," Cruz told CNN as the bus rolled through one of the most rural parts of the Hawkeye State.

"We're working hard to earn the votes of every man and woman here in Iowa," he said.