Bhd735, your daily budget does not directly influence your ad's position. It is your Max CPC that will have that effect.
So, as a rule, raising your Max CPC will tend to move you up the page, and lowering it will tend to move you down. However, this does not happen instantly, as noted below.
So - there are a couple of delays that you'll want to be aware of.
Firstly, when you make any change to your account, there are lots of severs that need to update. So, when you make a change, while it will be changed right away in your account, there will be server delays until the change is fully updated through the live site. This can vary from a few minutes to a few hours, depending on traffic.
Secondly, there is a three hour delay before your account stats are updated. So if you get a click in this instant, you won't see that click in your account for roughly three hours.
Also, be aware of the 'date range' you're looking at. The shortest period for which you can see stats is 'Today', which reflects all the time between midnight PST, and about three hours before you are checking.
So, if you make a change to your Max CPC in this instant, and then check using the date range of 'Today', you are seeing stats that include lots of hours at the old Max CPC too, and none at the current Max CPC.
To get a really clear picture of how a change is impacting your stats, it is best to wait until you have had a full 24 day at the new settings, and then look at the stats for that 24 hours.
Hope that makes sense.