Larry Summers, formerly the front-runner, recently withdrew his name from consideration after Democrats on Capitol Hill expressed their opposition to his probable nomination.
Meanwhile, Durbin also expressed concern about the potential of a government shutdown saying the chances are "getting larger."
The Senate passed a continuing resolution on Friday but House Republicans are uncertain about how they will proceed and will meet Saturday to carve out a strategy.
"If we turn the CR, the simple extension of government spending or even the debt ceiling into a political bargaining, we're finished," Durbin said.
"We'll do this every time, maybe five or six times a year. What's that going to do to us as a nation, to our government, to our reputation or to our economy? This is bad politics."