The immigration debate is a classic case in point of why the Senate was instituted by the Founders. The House passed a lousy and unworkable bill that was focused far more on exacting punishment than in solving the problem. In short, it pandered to a very vocal minority.
The Senate was created to make sure that there was not a rush to enact legislation. Not only are the rules of the Senate designed to allow a minority of Senators to slow things down, the re-election of the members of the Senate is staggered, so as to allow the passions engendered by a vote on a hot-button issue to not only cool, but it also insulates Senators - allowing them to take the long view of an issue.
In essence, Senators like Sam Brownback are not as vulnerable to being targeted for a purge as someone in the House of Representatives, like Chris Cannon. On immigration, the Senate has played a vital role. In essence, no bill that is enforcement-only (this includes the "enforcement first" bait-and-switch) will get through. To get any sort of immigration bill, the House will have to accept the needed large-scale plea-bargain/pre-trial diversion that Senators capable of insulating themselves from the talk-radio/internet-fuelled hysteria over the issue.
Sadly, as AJ-Strata notes, the Senate's role has been the subject of vicious comments and worse, and the House Republicans have chosen to sabotage any hopes for a bill. Some of the comments on the post are disgusting.