Fred Bauer has a thoughtful piece at National Review Online that's worth reading. He describes the dangers of today's condition of "bad-faith open borders," where "illegal immigrants are de jure rejected but de facto accepted."
One issue he didn't address was why we're in that situation. The reason for it is the same reason we have so much trouble achieving "sustainable harmony" (as he put it) on immigration: Each side sees the current stalemate as preferable to letting the other side prevail.
The core issue is whether there should be any limit placed on immigration. Supporters of immigration limits (high or low is not the issue here) obviously want the de jure prohibition against illegal immigration to be a de facto one too, with the laws consistently enforced. The other side is objectively (if not rhetorically) opposed to any meaningful limits on immigration, and so would prefer the de facto situation to become the de jure one.
This situation persists because the pro-limits side knows the de jure limits do at least exercise some control over the number of people moving here from abroad, even if they're not well enforced. The anti-limits side has as its goal the admission of as many people from abroad as possible, so a limbo status for them is fine so long as they're able to physically remain in the country. As Lincoln might have put it, both parties deprecate bad-faith open borders, but one of them would promote it rather than accept limits, and the other would accept it rather than let the borders be opened altogether.
Until there is consensus in the political class that capping immigration is morally acceptable (I would say mandatory, but I'll settle for acceptable), passing further legislation on the other questions — how many, what qualifications — is almost irrelevant.