(CNN) - President Barack Obama does not appear to be discouraged by Sen. Marco Rubio's Sunday morning statement that it is "premature" to consider a deal on immigration at hand.
White House Press Secretary Jay Carney brushed aside questions on Monday about "the comments that individual senators make about possible concerns they have - I would direct you to their offices."
"The president is absolutely serious about this. He has made clear that he is encouraged by the progress that's being made in the Senate and wants to see it continue and to produce a result," Carney said. "But he is absolutely confident that the approach we have taken of having the Senate “Group of Eight” move forward with bi-partisan negotiations and hopefully legislation has been the right approach."
Carney was referring to the “Gang of Eight” senators from both parties who have spent months attempting to negotiate a deal on comprehensive immigration reform.
Sen. Lindsey Graham, R-South Carolina, and Sen. Chuck Schumer, D-New York, said Sunday they expect to unveil legislation this week.
"It's got to be written up. We haven't signed off," Graham said on CNN's "State of the Union with Candy Crowley." "There are a few details yet, but conceptually - we have an agreement between business and labor, between ourselves. It has to be drafted. It will be rolled out next week."
Graham and Schumer, as well as Sen. Jeff Flake, R-Arizona, spoke Sunday after CNN and others reported business and labor groups had resolved their differences over a guest worker program outline, a key part of the final bill, and after Rubio’s statement.
"I'm encouraged by reports of an agreement between business groups and unions on the issue of guest workers. However, reports that the bipartisan group of eight senators have agreed on a legislative proposal are premature," Rubio wrote.
“We have made substantial progress" but the “Gang of Eight” draft "will only be a starting point" that will be considered and modified by the Senate as a whole, he added.
At the White House on Monday, Carney downplayed the role of any one individual, calling it a "cooperative effort" and maintaining the administration is "very much engaged."
He said the process would not have moved forward in the same way without Obama's influence.
"I think that we have chosen a path that makes a lot of sense which is giving room for the Senate to make progress in a bipartisan way on this issue, but I don't think that anybody should be under any illusion that we would not be where we are today making the progress that we have made if it weren't for the fact that the president has made clear consistently and very publicly as well as privately in conversation with rank and file members and leaders in Congress that this is a top priority for the country," Carney said.
Rubio, Graham, Schumer, and Flake are joined in the “Gang of Eight” by Sens. Michael Bennet, D-Colorado; Dick Durbin, D-Illinois; John McCain, R-Arizona; and Robert Menendez, D-New Jersey.