Answer
A reasonable estimate for the number of days you would spend counting is $12$.
Work Step by Step
If you counted $60$ numbers per minute, and you counted until you reach $1,000,000$, you would count for:
$1,000,000\div60 \approx 16,666$ minutes
In hours, this is equal to: $16,666\div60\approx277$ hours
This is equal to: $277\div24\approx12$ days
A reasonable estimate for the number of days you would spend counting is $12$.