Are immigrants a captured constituency of the Democratic Party?

It's not been a good year for immigrants and their supporters.  Last summer, the Senate passed a bipartisan comprehensive immigration bill, but elation soon gave way to frustration as the House refused to move on the bill and even a piecemeal approach died.  Then Eric Cantor (R-VA) was unceremoniously shown the door and many saw that development as the death blow for any hopes of immigration reform this year because he was replaced by an opponent that campaigned explicitly on an anti-amnesty stance. 

Last week, a memo declassified by the Clinton Library showed Rahm Emanuel advising then President Clinton in 1996 to out-Nixon even Nixon on law and order issues and specifically to deport "a record number" of immigrants.  Finally, two days ago, Obama announced a new emergency effort to streamline the deportation process to make it easier to return persons showing up on our southwestern border including unaccompanied minors.  Particularly egregious is that the Administration's new request for funding and change of policy is being made while the White House is also simultaneously referring to  the large number of child arrivals as a "humanitarian crisis", which would suggest a non-punitive response.  Are immigrants and their supporters a captured constituency of the Democratic Party?

Political Scientist, Paul Frymer argued in Uneasy Alliances Race and Party Competition in America that the two party system in the U.S. allows the Democratic Party to blow off the concerns of African Americans who are a numerical minority in order to appeal to moderate white voters who will help them win elections.  Frymer used the term "electoral capture" by which he meant:

[T]hose circumstances when the group has no choice but to remain in the party.  The opposing party does not want the group's vote, so the group cannot threaten it's party leaders with defection.  The party leadership, then, can take the group for granted because it recognizes that short of abstention or an independent (and usually electoral suicide) third party, the group has no where else to go.

Given that the Democratic Party seems to be trying to outdo the Republicans on toughness against immigrants, do immigrants and their supporters really have any good options except to stick with the Democratic Party and its schizophrenic immigration policies?   On the one hand, Obama has removed/deported a record numbers of immigrants and now is seeking to further streamline return/removal requirements.  On the other hand, Obama also created a program that Deferred Action for Childhood Arrivals, giving certain immigrants reprieve from enforcement. 

On balance though, it would not be accurate to consider immigrants a captured Democratic constituency, for now.  One reason is that many of the GOP leadership and even the rank and file  of the party do not oppose immigration reform--but a vocal and vociferous Tea Party wing does.  Indeed most Republicans realize that given the electoral calculus, moving on immigration policy has to happen at some point so the party does not continue to hemorrhage Latino voters and lose national elections repeatedly.  So it's not out of the question that the Republican Party would support immigration reform.  And, it also cannot be said that the Republican Party does not want the immigrant vote, quite the opposite.  BUT...while the GOP figures out how to deal with its Tea Party wing, the immigrants are temporarily captured by the Democratic Party.

Even if immigrants are not permanently electorally caputred yet, the two party system is one of the main culprits in enabling the continued lack of much needed immigration reform, and, indeed a lack of any bold legislation, to drag on now for several more years.  The structural incentives are such that both parties' main goal is to appeal to the median/moderate voters first to get themselves reelected before being responsive to a minority constituency on a controversial topic.