As the government shutdown drags on with little hope of a quick resolution, a situation involving the U.S. military could push the warring factions in Washington to come to an agreement.

No, soldiers won't be called into duty to force Congress to get back to work.

However, a looming paycheck scheduled in the middle of October for the 1.3 million active-duty members of the armed services might convince legislators and the White House that missing the date won't be worth the political cost.

"We believe the military pay date on Oct. 15 could be an important forcing event for a compromise to restore funding and expect the shutdown to end by mid-October," Goldman Sachs economists Ronnie Walker and Alec Phillips said in a client note.

The Wall Street firm noted that prediction

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