Let's just stipulate I'm tempting the fate of the GOB by posting this. So stipulated, we go forth.
Such a feat is doable, but I don't like the odds -- both teams are playing easy schedules for the time being.
From now until then, the Cubs play a game against the New York Mess, then three against the Pirates in Pittsburgh, then three against Cincinnati and three against the Untuckers at home before they go to St. Louis.
If the Cubs go just a game over .500 against everyone else, which I think is extremely likely against that "competition," and assuming three losses against St. Louis, that's a 6-8 record for them from now through the Cardinals clinching win on the 20th. Under these circumstances, the Cardinals would have to go 11-3, including that win on Sunday Night, to clinch at home against Cubs.
I like their opportunity to clinch against Houston more; in this decade alone, the Cardinals clinched against the Astros in 2000, 2001 (the infamous tie) and 2002.
If my math is incorrect, I deeply apologize.