The quick-moving conversation on whether liberals have anything to say to libertarians who believe corporate power is only dangerous when united with state patronage is an interesting one, and worth thinking seriously about. The libertarians involved argue that liberals -- many of whom want to extend, enlarge, or at least perpetuate state power -- are unwittingly but unerringly strengthening the corporations they seek to constrain. Many of the liberals involved think that's nonsense.
Part of the problem here is the simplicity and inadequacy of "Big Government" as a descriptor for much of anything. You can have a huge, interventionist, and corporatist government that doesn't do much to advocate for the public interest, but is nevertheless interventionist in nature and monumental in scale. As LB points out, after the Pinkertons would finish beating strikers, the police would throw the bloodied laborers into jail. That was Big Government, but not in the sense that the left means it.
At other times, government has been a pretty determined enemy of corporate power. It shattered Standard Oil, broke up AT&T, and curtailed Microsoft. It passed seatbelt laws, the Clean Air Act, and opened the door to unionization. It worked to elevate the interests of society over those of business. But yes, as the libertarians say, it can be as evil as it can be good. That warning suggests that it's not the size of government, but the type of government, that matters. Many libertarians reject the possibility of a positively-oriented state -- capture is inevitable. Liberals are fundamentally more optimistic on that front, and note that, in any case, the small government ideology has proven to do little but rechannel the state's efforts into promoting corporate power. So if liberals focus on the possibilities for restoring elements of the progressive movement into the state, they do so because nothing else has proven even partially capable of counterbalancing corporate power. Government may be a blunt tool, but it's the only one we've got.