Is it necessary to give more than two weeks notice?

In the company handbook for my current company, it says that non-exempt employees should give two weeks notice if leaving their position, but exempt employees should give at least 30 days notice.

I understand this being helpful to the company in creating a transition plan for a role with a large amount of responsibilities, but if you give the standard two weeks notice if some future potential employer calls them to verify employment, is it likely that they would hold it against me?

I don't really see companies looking to hire someone immediately for a new role being willing to wait a full month to start. Has anyone been in a similar situation?

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