The 27th Amendment actually has a fascinating history in that it was drafted by James Madison in 1789 but wasn't ratified until 1992.

So back in 1789... the question of congressional pay took up several days of debate. First, there was the question of whether legislators should be paid at all. Benjamin Franklin was a strong proponent of an unpaid legislature, as he feared paying legislators would encourage the "bold and the violent" to run for office. However, he was in the minority as most of the founders believed that only the wealthy would be able to afford to serve in an unpaid legislature. So the decision was made to pay members of the House and Senate.

The second question was then who would determine how much members were paid. Allowing members to set their own pay without any sort of limitation would allow them to enrich themselves. But the alternative of allowing the president to determine congressional pay was a non-starter, as that was seen as a major issue in England, where the King could basically buy off members of parliament. The founders did not want to give the president that kind of power over the legislature. So the compromise was to allow members to control their own pay, but prevent any increases from taking effect until after the next election. The thinking was that if members decided to give themselves a raise, they wouldn't be able to benefit from the pay increase unless the voters decided they deserved it and reelected them.

Madison actually drafted 19 amendments for the Bill of Rights. 17 of them passed the House and 12 passed the Senate and were sent to the states for ratification -- the ten amendments that would become the Bill of Rights, an amendment tying the size of the House of Representatives to the population, and the congressional pay amendment. Only six states (Maryland, North Carolina, South Carolina, Delaware, Vermont, and Virginia) voted to ratify the congressional pay amendment and so it was not included. However, the amendment did not include a deadline for ratification (as some later amendments have).

Fastforward to 1982... In the interim, two states ratified the amendment in protest of different congressional pay raises (Ohio in 1873 and Wyoming in 1978) but it was largely forgotten. An undergraduate at the University of Texas (Gregory Watson) wrote a paper for a class arguing that the pay amendment could still be ratified. He got a C on the paper and decided he was going to prove his professor wrong by getting the amendment ratified. Watson started writing letters to members of Congress to ask about the amendment and was mostly ignored, but Senator William Cohen passed the amendment on to people in the Maine Legislature, which ratified the amendment in 1983. He kept at this letter-writing campaign for ten years until the 38th state (Alabama) ratified the amendment in 1992. (And Watson got his grade changed to an A in 2017.)

In terms of controversy, the content of the amendment itself had broad bipartisan support. During the 1980s and early 90s there was a fair amount of public backlash over a series of congressional pay raises and other scandals involving the post office and congressional bank, which made it relatively easy for the states to ratify the amendment. In 1989 Congress voted to give themselves a 51% pay raise from $89,500 to $135,000 a year, which was opposed by 82% of the population. Due to the backlash, they pulled back to $98,400, but then passed a law to create automatic cost-of-living adjustments so they would be able to increase their pay without taking an unpopular vote. Basically, the political conditions were such that voting against limiting members pay was the fare more controversial option.

There was (and is) still some controversy over the 27th amendment, but it's largely over the process. While the amendment did not include a ratification deadline, there are some legal scholars who question whether it's valid given that the House and Senate that voted to pass the amendment in 1789 represented a very different country than the 38 states that ratified the amendment by 1992. However, in 1992 Congress voted to "accept" the ratification of the amendment (unanimously in the Senate, 414-3 in the House) so it wasn't completely without contemporary congressional approval. The difference is that the Congress in 1992 wasn't proposing the amendment (which never would have happened at the time) and instead was forced into responding by the states.

ETA:

Sources: Constitution Center, Strickland (1993), Gregory Watson Interview on CSpan