Local load balancing and using cloud services when needed

Suppose a company has a set of web+data servers that are load balanced, but sometimes the application gets a burst that goes beyond server capabilities.

This would nicely mitigate the cost of cloud services to only use them when you actually need them. Otherwise in-house hardware suffices.

Question
Has anybody done load balancing of such bursts to cloud services? Is it at all possible? WHat would one have to think about to achieve such configuration?