The role of 'that'

In this view, deep spending cuts and a one-year modest tax reduction could result in the worst of all possible economic worlds: an inflationary recession. Thus some economic advisers are telling the White House to fight to the end for its tax plan - at the very time that the Administration is having trouble countering Democratic troops in line. The outlook is not only for along argument in Congress, but for divided counsel within the Administration.

I' don't know at all in the above sentence, what role the word 'that' in bold play.
I will appreciate any opinions.