The United States Constitution requires that the President must "take care that the laws be faithfully executed."
Probably the two Presidents who had the most trouble with this were Abraham Lincoln and Andrew Jackson.
All the Laws but One
by former Chief Justice William H. Rehnquist is about Lincoln's struggle with his duty to enforce the laws during the Civil War.
In a CSpan video, I have no idea if it still exists, Rehnquist mentions how President Jackson has been wrongly accused of not enforcing the law in at least one Indian removal case.
President Obama has an increasing list of lack of enforcement.
In the Afordable Care Act the administration is not enforcing the employer mandate, verification of eligibility for insurance subsidies, and will not require employer-provided policies to cap employees' out-of-pocket costs.
"Obamacare administrators continue to miss deadlines set by the health-care law -- 41 of 82 of them, according to Forbes's Avik Roy's reading of Congressional Research Service report."
The administration is also lax in enforcing the Dodd-Frank financial regulation law. "According to the law firm Davis Polk, the administration as of July had missed 62 percent of the deadlines in that law."