First there isn't such thing as opening the flood gates. Nothing in politics is forever and generally swings back and forth. So if the Democrats are on the right side and whatever happens happens it wouldn't all of the sudden make them the dominate party forever. If that was the case then African Americans would all be Republicans since they where the party that passed the Civil Rights Act.
As far as how they approach fixing immigration it has to start with softening their tone. Immigration reform is something that will happen sooner or later therefore they need to back off the harsh rhetoric that has been used. Stop with the laws in different states trying to crack down on it as they have proven thus far to be ineffective with the federal government blocking them soon as they are passed. That would greatly help the image of the GOP with Hispanic voters then beyond that start with small pieces. A full revamp of the system is going to be a very long drawn out process. So starting with something along the lines of the dream act would be helpful and both parties could agree on.
Beyond that it really depends on what Obama has in mind for his second term. Does he bring up Immigration reform after we get through avoiding sequestration? Or does he go after tax code reform? It is going to have to be an either or proposition I believe. They have probably a calendar year to get something major done before reelection season starts again. Once that happens I don't think anything major is getting done. The makeup of Congress after that will go a great distance in determining how to proceed. The House will almost assuredly stay in GOP control with 33 Senators up for reelection (20 D, 13 R). If by some chance the GOP picks up the Senate also then they would be able to be the party in charge when immigration reform occurs.
French writer Alexis de Tocqueville warned about when visiting this fledgling democracy in the early 19th century – that this "American republic will endure until politicians realize they can bribe the people with their own money."