同位语从句that省略问题

同位语从句that省略问题
原句：In a sign the government's role in the industry could become open-ended,the Treasury Department said Monday it had set up a separate program within the Troubled Asset Relief Program,a fund originally designed to help banks,to make investments directed at the auto industry.
提问 ----In a sign the government's role in the industry could become open-ended,1.sign 和 后面的 the governmnet's role .是不是同位语关系?如果是的话 为什么没 THAT 同位语从句据我所知That 是不能省略的 .
2.如果不是 ,请各位朋友告诉我这是哪个语法 知识点 如何
首先，我想 the government's role in the industry could become open-ended,是 对 SIGN 修饰 说明的 所以 应该 是 同位语 并不是 什么 定语 从句的知识~但是 同位语 从句 明确 提出 ：that 引导从句是是 连接词 是不能省略的 所以 难道 美国人在平时使用 时候 常常 省略 是这样吗