This is from Dwight Goddard, an early 20th century popularizer of Buddhist texts. It’s meant to be a rendering of Dhammapada verse 21, which Buddharakkhita has as
Heedfulness is the path to the Deathless.
Heedlessness is the path to death.
The heedful die not.
The heedless are as if dead already.
Buddharakkhita’s translation is very literal.
In his drive to popularize Buddhist teachings, Goddard was keen to make Buddhism sound more Christian, hence his “Buddhist Bible” and the change from “path to death” (maccuno padaṃ) to “short road to death” is no doubt meant to evoke Matthew 7:13–14, which reads:
13 “Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it. 14 But small is the gate and narrow the road that leads to life, and only a few find it.
The term “idle” also appeals to Christians, with the religion’s emphasis on “good works.” “Diligence” or “heedfulness” (appamāda) is more of an internal attitude of watchful mindfulness, and while it may lead to external good works its function is to protect the mind against unskillfulness.
So this is one of these occasions where the Fake Buddha Quote arises because of a distorted — in this case, perhaps, deliberately distorted — translation.
The Fake Quote is found on quotes sites, and in dozens of books, mostly of the New Age or self-help varieties.