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Doesn't matter how you use the $$ that are gifted - it is still a gift.  Should not be any issues with the IRS if what is gifted is cash as there is should not be any dispute on the FMV of cash.

I am assuming that the home will be titled in your name.  Additionally, once the house is built and they live there, the IRS could contend that the parent is receiving a gift from you in the form of free rent, however, that value I would assume is less than the $14,000 exemption.  I don't see this as an issue here.
*A reminder that posts in a forum such as this do not constitute tax advice.
Also keep in mind the date of replies, as tax law changes.