In response to a Rasmussen poll cited here, Nicholas Thompson from the White House Office of Strategic Initiatives e-mails:

In response to the post regarding the Rasmussen poll, it should be noted that the plan proposed in the question does not include many of the components included in the actual plan. Rasmussen asked respondents:
“A different proposal has been made that also includes a fence along the Mexican border, more border patrol agents, strict penalties on anyone who hires illegal aliens. This proposal, however, would also offer illegal aliens a path to citizenship if they pay back taxes and other fines. Would you favor or oppose this proposal?”
In order to have an opportunity for citizenship, undocumented workers will have to pay a total of $5,000 in fines, pass multiple background checks, complete accelerated English and civics requirements, go back home to apply in their home country, demonstrate merit in the new merit-based green card system, AND go to the back of the line behind those who applied lawfully. Clearly it is a much more onerous process than the text of the question suggests. Take a recent bi-partisan poll that did include more components of the plan, conducted by The Tarrance Group (R) and Lake Research (D):
75% of American voters said they would favor a plan that: provided resources to greatly increase border security; impose much tougher penalties on employers who hire illegal workers; allow additional foreign workers to come to the US to work for a temporary period; create a system in which illegal immigrants could come forward and register, pay a fine, and receive a temporary work permit; and provide these temporary workers with a multi-year path to earned citizenship, if they get to the end of the line and meet certain requirements like living crime free, learning English, and paying taxes. Only 17% opposed this plan.
This is not to slight Rasmussen. Like many polling agencies, they were seeking the broad thematic of support for an immigration plan with a path to citizenship. However, there is a significant difference in opinion when Americans are given more details of the plan- not just broad rhetoric.