The cool thing about blog giveaways is you can usually tell now many people are entered. The less entered, the better your chances to win. Here's some I found with low entries ending soon.
If you have a giveaway with less than 60 entries per prize ending in the next 6 day, please submit it here.
A lot of this week's giveaways have multiple winners, which really increases your chances!
Ends July 6
Ends July 8
Ends July 10
Cubs Stuff (At least 11 Entries)* - US
*I could not tell how many instagram entries, or twitter ones.
I could tell comments and knew of at least 2 on twitter.