Story highlights The White House chief of staff criticized a bipartisan immigration bill proposed last week

John Kelly's criticism was that the the House and some key senators were not consulted

(CNN) White House chief of staff John Kelly on Wednesday defended the President's rejection last week of a bipartisan Senate immigration bill, saying it wasn't as inclusive as the President asked for.

Speaking to reporters in the Capitol in between four back-to-back meetings on the issue with lawmakers, Kelly declined to answer whether he and staff had misguided the President, as Sens. Dick Durbin, an Illinois Democrat, and Lindsey Graham, a South Carolina Republican, alleged after their proposal was rejected.

"That deal that came over was supposed to be two things: bipartisan and both sides of the Hill," Kelly said. "And it was bipartisan in the sense that there were several Democratic and Republican senators, but there were a number of other senators that had been involved in this from the beginning, (Sens. Tom) Cotton and (David) Perdue is an example, (Thom) Tillis from North Carolina, that were not consulted. And the House was not consulted at all."

Durbin and Graham crafted the bill with two other Republicans, Sens. Jeff Flake and Cory Gardner, and Democrats Sens. Michael Bennet and Robert Menendez. Tillis and Republican Sen. James Lankford had been meeting with the group but were not included in meetings after the new year over perceptions about lacking a sense of urgency. Cotton and Perdue are supporters of a hardline proposal to slash legal immigration supported by President Donald Trump.

Kelly said that in the meeting, where the President made the now-infamous "shithole countries" comment, Trump's sense was the Durbin-Graham bill "fell short."

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