Estimates by Moody’s Economy.com, presented in recent Congressional testimony, suggest that of the $12 trillion the government has committed to fight the financial crisis and recession, the final tab to taxpayers will approach $1.2 trillion.

在最近的国会听证会上提出的关于穆迪旗下Economy.com的评估报告表明，政府承诺投入用于应对金融危机和经济衰退的12亿美元的资金，纳税人最终将承担的部分将逼近1.2亿美元。

这里的that 和 of之间并无关系，that是跟在suggest 后面宾语从句的引导词， of the $12 trillion 应该在$1.2 trillion后面，这里前置了而已。

正常结构应该是：
Estimates by Moody’s Economy.com, presented in recent Congressional testimony, suggest that the government has committed to fight the financial crisis and recession, the final tab to taxpayers will approach $1.2 trillion of the $12 trillion（used to fight the financial crisis and recession.
在最近的国会听证会上提出的关于穆迪旗下Economy.com的评估报告表明，政府承诺应对金融危机和经济衰退,，纳税人最终将承担12亿美元舒困资金中的将近1.2亿美元。

of the $12 trillion前置后，就把政府打算用12亿解决问题这个意思表达出来了。而如果是正常语序，意思似乎有所断开，需要更多的词汇去表达清楚。这正是英语的灵活之处。

至于that of, 还真有这么一个结构，其中THAT是代词,与关系代词无关,它代替了前面的某个内容.
The product in her factory is better than that of mine.

that此处代表了product

We were talking about China and Hongkong's future and that of their patrons.
这个that 代替了future