Updated

This is the latest in a Fox News series examining the controversy over gun violence and gun control. 

In radio and billboard ads across the country, the federal government is telling potential gun buyers "don't lie for the other guy." The campaign message is intended to stop those with clean criminal records from buying firearms for felons who legally can't buy guns on their own.

The message underscores the full-court press in Washington to adopt sweeping new gun control laws, from universal background checks to a ban on military-style rifles and large ammunition magazines.

However, recent studies show the Obama administration has not enforced many gun laws already on books -- with gun crime prosecutions hitting a decade low in 2011, down 40 percent from their peak under President George W. Bush in 2004, according to federal data crunched by Syracuse University. The SU study prompted 23 House Republicans on Friday to call on President Obama and Attorney General Eric Holder to prosecute more people for gun-related crimes.

"It is imprudent to simply call for new laws without examining the efficacy of the current laws," wrote House Judiciary Committee Chairman Bob Goodlatte, R-Va. "We must all be looking for ways to prevent senseless acts of violence and the taking of innocent life, but the best place to start would be enforcing the laws that Congress has already enacted."

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The Syracuse study found the number of federal weapons prosecutions fell from about 11,000 in 2004 to about 6,000 under the Obama administration in 2011 -- and ticked up to 7,770 in 2012.

The GOP letter also cited data from the National Criminal Justice Reference Service (NCJRS), which found in 2010, of 6 million Americans who applied to buy a gun, less than 2 percent -- or 76,000 -- were denied. Of those, the ATF referred 4,732 cases for prosecution. Of them, just 44 were prosecuted, and only 13 were punished for lying or buying a gun illegally.

"If the prosecution of people lying on forms is really a priority for the president, then all he has to do is say, 'I want my federal law enforcement officials to prosecute these kinds of cases,'" former Attorney General Alberto Gonzales told Fox News. "Obviously there is a different level of priority given to these type of crimes in this administration compared with other administrations."

Justice Department sources argue the attorney general has finite resources. DOJ prefers to prosecute prohibited persons who actually obtain guns illegally, who've gotten around the background check system, rather than just those who just lie on the form, which is also a crime.

A source also said so-called "lie and try" cases have little jury appeal. They are essentially about lying on a form where the person was ultimately denied the ability to purchase the gun. Juries, in these cases, have a tendency to question whether any harm was done, because the individual did not get the gun.

Prosecutions for making a false statement when buying a gun are down 29 percent from five years ago, while prosecutions for illegal possession are down 14 percent, according to federal data. Penalties are also light. Data compiled by the U.S. attorney's office shows a third of those charged with gun crimes serve no jail at all, and those who do typically only serve one to four years of a possible 10-year sentence for lying or illegally possessing a firearm.

"I think when we punish the bad guys we are protecting the good guys," said Republican Rep. Scott Rigell of Virginia. "That is the essence of this bill. When four out of 10 straw buyers suffer no meaningful consequences for what they did, we have a problem."

Rigell is one of four lawmakers proposing a bill to make straw purchases a federal crime. The bill would also increase the penalty from 10 to 20 years.