Nope!
Politifact looked at Cruz's charges:
Our ruling
We found that at least seven presidents -- including some of the nation’s most admired occupants of the White House -- acted, at least on occasion, in ways that ignored specific laws or constitutional protections. It is not accurate to say, as Cruz does, that Obama would be "the first president we've ever had who thinks he can choose which laws to enforce and which laws to ignore." Presidents have done so frequently, and historians expect that they will continue to do so. We rate the claim False.
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EDITOR’S NOTE, March 11, 2014: After we published our story, Cruz’s office provided the following response:
"Since the dawn of the republic, the president and Congress have resisted attempts from each other to encroach upon their constitutional powers. Many presidents have asserted, and have abused, executive authority. No one is arguing that President Obama is the first to make this mistake. As Sen. Cruz has detailed in three reports, a Wall Street Journal op-ed, and a brief before the U.S. Supreme Court, no president until President Obama has ever claimed the authority to ignore the explicit text of statutes passed by Congress and unilaterally replace that text with whatever the president wishes. From Obamacare to immigration, to same sex marriage, to marijuana laws, President Obama’s willingness to ignore or alter law is unquestionably outside the scope of executive power. It amounts to legislating, pure and simple."
However, we don’t agree that there’s a significant distinction between "abus(ing) executive authority" and a "willingness to ignore or alter law," so we feel comfortable with the historical examples we used to analyze Cruz’s statement. We’re standing by our original ruling of False.
https://www.politifact.com/truth-o-meter/statements/2014/mar/10/ted-cruz/ted-cruz-says-barack-obama-first-president-who-thi/