This bill would discourage frivolous lawsuits, which everybody on earth agrees is good, but it accomplishes that goal by making it impossible for some people to seek justice in the legal system. There are already systems set in place where you can sue someone and if you lose, have to pay their attorney fees. If this passes, fewer people (specifically fewer poor people) will be able to sue.
For example, say you're hit by a Microsoft employee driving a Microsoft company car during the course of his duties. It's basically 30 percent your fault and 70 percent his fault. You rack up 100K in repair bills and hospital and surgery costs. So your lawyer can estimate that you'll get 70K from Microsoft (assuming a 60/40 fee for the lawyer, you get 42,000$ after you pay him). Great, but there's a 10% chance you'll get nothing. That's OK, that's why the attorney works on a contingency basis - if you lose you don't pay him. The attorneys for both sides go to court (or settle or w/e) and the legal system provides justice.
But, if this passes then it plays out this way: same accident, same everything. Except you know Microsoft is willing to spend 40K in their defense costs. Now, you have to wonder if you're willing to take a 10% chance that you'll be out 40K on top of everything else. It's a fact that fewer people will be willing to take that chance, and more people will settle for less. Which has the end result that Microsoft can injure people cheaper, and the poor will receive a less fair outcome since the process is stacked against them from the beginning.
(not that people at Microsoft sit around a board table and plan to injure people, but they are profit-driven, thus the more expensive something is the more care they take to avoid it)
There's a delicate balance between the injustice of a frivolous lawsuit damaging an innocent party and the injustice of legislating that fewer people will be allowed to sue, and those that can afford to will be willing to settle for less money.
The bill fits neatly into the political philosophy (that many conservatives have) that large corporations shouldn't be held as responsible as they are now. They don't have anything against people, or poor people, but they think that society is best served when corporations are unfettered. If that means paying smaller penalties for injuring people, so be it. The bizarre part is that they sell this philosophy using fear to the very people they're injuring under the guise of "smaller government". I suppose that's not totally true, the most bizarre part is that people are allowing themselves to be scared into supporting this philosophy.
In short, fewer frivolous lawsuits is a good goal, but it shouldn't be accomplished by denying justice to the most vulnerable in society. This bill clearly sacrifices the most vulnerable to "solve" a near non-existent problem by using legislation to pervert justice.