With a lot of difficult problems __the president is
问题描述：
With a lot of difficult problems __the president is
having a hard time 用to settle 不用to be settle
答
settle和to be settle的不同：
在这一点上,用法和have sth.to do/to be done一样,前者表示这句句子的主语自己去做这个sth,而后者则表示是“让别人去做”
比如说,同样是洗衣服
妈妈要洗很多衣服：Mom has a lot of clothes to wash.
妈妈要把衣服（送到洗衣店里）洗掉：Mom has a lot of clothes to be done.
那么现在回过来看原句,“总统忙得焦头烂额”那么显然,这些“麻烦的问题”是由总统自己解决的,那么就应当使用to settle而不是to be settle了.