So... a worse version of a price comparison website? Instead of showing the best price, you want to show only a price better than customer's previous? Why wouldn't people just use a normal price comparison website which shows the cheapest offer?
If a supplier has the best price in the market, it makes sense for him to advertise this fact. So either a supplier is losing potential money by listing minimum price only with you, which is extremely unlikely, or your lowest price will be equal or higher than the lowest on price comparison websites, thus making your website useless. The same people who may use your site are already using price comparison websites.
I can see your idea working if you could somehow display your offer to people who aren't shopping for lowest price while they're buying somewhere else, but how? I think some adware did exactly that...
An another existing variation of that idea is decreasing the price when customer changes his mind at the last moment.
There is a company in Australia called bing lee (http://www.binglee.com.au) that allows you to do this. You can either barter in store or via their chat on their website.
I don't see this idea being successful easily. Driving people to your site and making them interact with you would be difficult. I personally couldn't bother with such a site, too much effort. I'd rather see whatever is cheapest on a few different sites and go from there.