Clearly the amide will be unreactive given the poor quality of the leaving group and poor electrophilcity due to delocalization. However, does it react with organolithiums for example?
Amides will react with three equivalents n-butyllithium to give nitriles via geminal lithium oxyimide intermediates (J. Org. Chem., 1967, 32 (11)). n-butyllithium is a strong enough base to deprotonate the molecule twice at nitrogen and once alpha to the carbonyl group. Grignard reagents may well behave similarly.
I do not think this is a particularly useful transformation though because n-butyllithium is a rather indiscriminate reagent. There are a wide range of other methods available - see this paper if you're interested.
In the special case of a N,O-dimethylhydroxyamide, you can make ketones using either.
For a N,N-alkyl, a N,N-diaryl or a N-alkyl-N-aryl amide that what will happen is that the grignard will react attacking the carbonyl carbon. This will form R''C(NR2)(R')-OMgX from RMgX and R''-CONR2.
What we normally do is to treat the product with dilute acid, this will then convert the initial additon product into either a ketone or an aldehyde.
One common method of making aldehydes is to react Grignards and other similar reagents with DMF, then treating the intial product with aqueous acid.