1.at least是一个介宾词组,类似于副词,在句中一般做状语.
它可以放在句首,所以说其后是可以跟句子的.
At least I have you.这种句子是可以的.
再如：At least you look happy.至少你看上去高兴.
At least I think so.至少我认为是如此.
2.at least作为一个状语,其位置非常灵活,一般放在其强调的部分之前.
所以楼主给的例子中,从句意来看,at least就是修饰宾语的.
它还可以修饰其他成分,如以下几个例子：
1）修饰主语
At least fifteen were killed.
至少十五人死亡.
2）修饰宾语
Authorities are reporting at least 30 arrests.
当局表示,至少有30人被捕.
3）修饰状语
He went at least once a week.
他至少一周去一次.