The Fugitive Slave Act was one of the bills that in combination are known as the Compromise of 1850.

After the Mexican-American War (1846-48) the United States acquired more land, and it became a subject of extreme contention about whether or not to expand slavery into the new areas of the country. Debate between the Southern slave states and the North was extremely contentious, to say the least. The sense at the time is that the US was verging on a violent schism and civil war over the issue.

Senators Henry Clay (of Kentucky) and Stephen Douglas (of Illinois) worked out a series of bills that essentially made a "good enough" compromise to keep the republic together. While we now know that they didn't prevent the Civil War, at the time it was lauded as one of the great moments of debate in the history of parliamentary systems, and the country was saved for at least a few more years.

The fugitive slave act was quite unpopular in the North, especially later (after passage) because it made abolitionist states complicit in slavery. However, the US Senate was essentially (and explicitly) designed to be nearly immune to public opinion, so as one of a package of bills designed to save the country from civil war, it passed overwhelmingly. In a way, the Fugitive Slave Act may have actually strengthened Northern attitudes, because it made slavery harder to ignore.

Sources:

Michael Holt, The Fate of Their Country

Robert Caro, Master of The Senate

It's a pretty good episode, isn't it? I'm told the guest is thoroughly pleasant company, handsome, and can't continue with a straight face now. :)

The Fugitive Slave Act was massively unpopular in the North. It was also tremendously popular in the South. Zero southern members of Congress voted against it, which is a good start. Since the South is at parity with the North in the Senate, two senators per state and an equal number of states, if everyone votes with their section then they're basically there. That's what happened; zero Southern members of Congress vote against the Fugitive Slave Act.

The House is different, but not that different. The South gets representatives on account of, but by no means for, 3/5 of its enslaved population. That's padding against demographics, which grows more crucial as the nineteenth century goes on because the North does grow faster. The whole South together accounts for 40% of the House. Democrats, who are pushing the measure and the more proslavery party, can edge that up to 48%. Southern unity and party pressure only go so far.

To cross the finish line, the Fugitive Slave Act needed what every capitulation to slavery required: sellouts from the North. Getting them usually was not too hard because of the other thing that greases the wheels in proslavery directions for the whole antebellum: white Southerners care massively about slavery. It's the central, defining institution of their civilization. Threats to it, even potential threats, are existential. If you don't fight hard enough for slavery, you will have a challenge winning re-election.

Most white Northerners have nothing even close to that level of commitment to antislavery. For the most part, whites in the section just don't care as long as they don't have to look at black people. People for whom antislavery is their main issue are in a distinct minority. Thus there's always political space for Yankees to vote for slavery, particularly in states that border the South and out in the west. In the Northern Democracy, the vote goes 27-16 for the law. Democrats from states not bordering on slavery, the Upper North, split 7-6 for it. The Lower North go 20-10. By contrast, showing the stronger party institutions and greater domination of the party by the South, Northern Whigs vote 71-3 against it. Taking the whole North together, 70% vote no. That 30% that vote yes, plus the whole Southern delegation, gets the bill sent to Millard Fillmore's desk.