Date  Budget
0 2018-02-24 11:20:16    6.35
1 2018-02-24 11:34:10    5.85
2 2018-02-24 16:41:12    3.85
3 2018-02-25 00:55:18    1.10
4 2018-02-25 01:36:47   -0.90
5 2018-02-25 03:12:51   -1.90
6 2018-02-25 11:29:31   -2.90
7 2018-02-25 18:20:35   -3.65

near_zero = df['Budget'].abs().min()

near_zero = df.loc[df['Budget'] > 0, 'Budget'].min()
print (near_zero)
1.1