Customers are human, which means that they sometimes bend the truth. Here are the most common lies that customers tell and how to use them to your sales advantage:
No matter how much a customer claims to "love" their current vendor, they're always willing to consider a better alternative. Your job is to make it clear why you're the better alternative.
Unless the customer is actually bankrupt, what this really means is "other projects have a higher priority." Your job is to explain why your offering is more important than what's already been budgeted for.
This is usually wishful thinking. Even in "Mom and Pop" operations, "Mom" can veto decisions that "Pop" makes. In big companies, decisions are always by consensus. Your job is to discover (and sell to) all the stakeholders.
This is how customers say "I'm busy so get lost" without being rude. Your best bet here is to agree to send the information but also ask something like: "Just out of curiosity, what are your priorities in this area." Keep the conversation going.
Well, probably not all THAT sorry because clearly something more important came up. Fortunately, social convention now puts the customer under an obligation to do something to make up for wasting your time.
Sorry, but in every sales situation that goes out for bidding, there's somebody who's got the inside track (usually they wrote the RFP). Your job is to either be that somebody or earn the write to tweak the RFP.
The customer is well aware that there's a perfectly good reason (like better service or more features) why your offering costs more. If not, then the problem lies in how you're presenting and positioning your offering.
These last minute demands are how customers test to see that they've negotiated the best deal. If you fold and give the discount, they'll know you were about to cheat them. If you stand your ground, they'll sigh in relief and pull out the checkbook.