It's unclear whether you're asking about "jerry-built" or "jury-rigged", so I'll give the etymology (word history) for both.

from WordOrigins.org :

Jerry-built, meaning to temporary or shoddy construction, dates to 1869. The OED2 hazards a guess that it may derive from the name of a builder who was notorious for poor construction. An 1884 source (unconfirmed) says that the phrase is in reference to a particular construction project on the Mersey River in Britain.

From Etymonline.com :

jerry-built
1869, Eng. dial. jerry "bad, defective," a pejorative use of the male nickname Jerry (a popular form of Jeremy), or from naut. slang jury "temporary," which came to be used of all sorts of makeshift and inferior objects (see jury (adj.)).

However, we should not confuse "jerry-built" with "jury rigged". While they sound similar, their meanings are DIFFERENT.

According to WordOrigins.org:

Jury rig, while similar sounding, has a slightly different meaning, emphasizing the temporary nature of the solution and can imply an ingenious solution done with materials at hand. Jerry-built, on the other hand, is often used for a permanent, but poorly built, construction and has no positive connotation.

The origin of jury rig is nautical and dates to 1788. It is from the nautical term jury mast. This term dates to at least 1616 and refers to a temporary mast erected to hold sail when the normal mast has been lost due to storm or battle. It is commonly thought that this sense of the word is a clipped form of injury mast, but no evidence of this longer term has been found. This form of jury is etymologically unrelated to the jury that sits in judgment at a trial.

and now from the word detective:

Dear Word Detective: I'm curious about the word "jerryrig," as in to make do with materials on hand. I recently saw it spelled "juryrig," but the context seemed to be the same. Is the correct spelling "jerry" or "jury" and what is the origin of the word? What, if anything, does it have to do with a rigged jury? -- Jill Fitzpatrick, via the Internet.

Not much, if anything. Then again, some of the juries running around out there these days could probably do with a little jury-rigging, perhaps a little money under the table for paying attention to the simple facts of the case. Between turning certain people loose in the face of mountains of evidence and fining other folks millions of dollars for lying on their job applications, juries are rather rapidly reaching a level of credibility formerly attained only by UFOlogists and mail-order psychics.

In any case, the "jury-rig" (it is usually hyphenated) you're asking about has nothing whatever to do with juries in the judicial sense. "Jury" was originally a naval term for any makeshift contrivance substituting for the real thing in an emergency, most commonly found in the term "jury-mast," a temporary mast constructed in place of one that had been broken. There's some debate about where the word "jury" in this sense came from, with the leading (but unverified) theory being that it was short for "injury."

To say that something is "jerryrigged" is to mix idioms a bit, because the proper term is "jerrybuilt." A "jerrybuilder," a term dating to 19th-century England, was originally a house builder who constructed flimsy homes from inferior materials. The "jerry" in the term may have been a real person known for the practice, or may be a mangled form of "jury," as in "jury-rigged." I tend to think that "jerrybuilt" arose separately from "jury-rig" simply because their senses are slightly different. Something that is "jury-rigged" is concocted on the spur of the moment to meet an emergency, but something "jerrybuilt" is deliberately constructed of inferior materials to turn a quick buck.

http://www.word-detective.com/back-g2.html

well... it all started when i married a guy named jerry. any time he "fixes" something it ends up being worse off than it was before but it still works. therefore, jerry rigged it.

Seeing as, according to several soures I've been able to find, the terms "jury-rigged" and "jerry-rigged" both pre-date America, I think its Pavementaled who's being a bit derogatory with the comment about Americans.

"Jerry Rigged"
is in fact a derogatory term, but not for Germans, for Special People, or Retards. It comes from the Jerry Lewis Telethon for "Jerry's Kids". It is not necessarily to describe something as done cheaper, but done shoddy.

This is wrong. Wrong I tell you... as far as the jerry-rigged is concerned. "Jerry" is an derogatory name for a German Person. Just like the N-Word is for a Black Person. Both have been used, N##g#r Rigged and Jerry Rigged are both forms of slang used to describe something that has been put together using an alternative method usually done cheaper than doing it correctly. Americans like to be derogatory.