The poem is apparently by Mary Howitt (1799-1888)/ The first verse goes like this:

“Will you walk into my parlor?” said the spider to the fly;
“’Tis the prettiest little parlor that ever you did spy.
The way into my parlor is up a winding stair,
And I have many pretty things to show when you are there.”
“O no, no,” said the little fly, “to ask me is in vain,
For who goes up your winding stair can ne’er come down again.”

The spider is a Zebra Jumping Spider.

For others waxing lyrical in June, please see here: http://form.pbase.com/viewtopic.php?f=16&t=48363