Can the President alone determine if something is Constitutional or not?" Since Holder is referencing that argument. Need an Attorny's opinion here perhaps.
Yes, the DoJ (at the direction of the president, or independent of the president) can (and has frequently in the past) concluded that "something" isn't constitutional. BUT, that's entirely different from a Court holding that "something" unconstitutional.
Generally, a DoJ opinion is just that. And, it's important to point out that opinion is not binding on any court, although the court can take such an opinion under advisement and can view it persuasively.
Congress does this frequently with their own Congressional Research Service. This congressional branch will issue opinions about the constitutionality of laws, or how laws are (or could be) applied unconstitutionally.
What the DoJ can't do, is decide that a law is unconstitutional, and then stop enforcing that law, or begin violating it some way. But, they can decide that they won't defend the law from current or future civil legal challenges.