I have heard people imply that there are parties that want to spam the block chain for some reason, for example to get more support for higher blocks.
How is spamming the block chain discouraged by the Bitcoin protocol?
It's not really.
Of course there are transaction fees, but in the situation you describe, where blocks are not already full, the supply of available block space must be lower than the demand, and so you should be able to create many transactions at low fees, and miners will put them in their blocks because low fees are better than none at all.
Or, if you are a miner yourself, or have a deal with one, you can fill up your blocks with your own transactions, with whatever fees you like, since they are all going back to you. (There is a slight risk here: if you make the fees significantly higher than the market rate, the next miner may choose to orphan your block and include those transactions in her own; then she gets to keep the fees you were planning to pay back to yourself.)
There is a slight disincentive for such a miner in that large blocks propagate slower and thus are slightly more likely to be orphaned.
Other miners might notice you are doing this, if you appear to be getting way more transactions in your blocks than anyone else, and so it might not help convince them to support larger blocks. But it doesn't really prevent the "spam".