Senate Majority Whip Dick DurbinRichard (Dick) Joseph DurbinSenate Republicans face pivotal moment on impeachment witnesses Democrats see Mulvaney as smoking gun witness at Trump trial Trump legal team offers brisk opening defense of president MORE on Sunday asked Minority Whip Jon Kyl to sit down and talk about comprehensive immigration reform.

The duo, appearing on "Fox News Sunday," didn't agree on much when discussing immigration -- Kyl said border security is the first priority and Durbin pressed for passage of the DREAM Act -- but Durbin made a pitch.

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"Here is the offer I'll make to Jon Kyl and John McCainJohn Sidney McCainConservative activist wins contest to represent New Hampshire at Republican National Convention Schiff shows clip of McCain in Trump impeachment trial Martha McSally fundraises off 'liberal hack' remark to CNN reporter MORE. I will sit down with you, I will work with you to have border security beyond what the president has done," Durbin said. "I will go even further to make sure that our border is safe, and to stop, as much as humanly possible, illegal immigration, if you will join with us in comprehensive immigration reform so that we can identify those living in this country, we can give the children under the DREAM Act an opportunity to have a good life in this country, and we can finally fix this broken system in good faith."

Kyl responded, "Dick Durbin and I sat down before to talk about things, and I'm very happy to do it on this very important issue. But I will say, we have got to secure the border in order to achieve these other results as well."

Senate Majority Leader Harry ReidHarry Mason ReidTensions between McConnell and Schumer run high as trial gains momentum The Trumpification of the federal courts Trump to rally evangelicals after critical Christianity Today editorial MORE (D-Nev.) has vowed to hold a vote the DREAM Act, legislation creating a route to legal residency — and ultimately citizenship — for illegal-immigrant students. 

The latest version of the DREAM Act, introduced Wednesday by Durbin, is nearly identical to last year's House-passed proposal which failed to pass the Senate. It offers a pathway to citizenship for between 1 million and 2 million illegal immigrants who came to the U.S. before the age of 16, have lived in the country at least five years, have a high school diploma or the equivalent, and enter college or join the military.

Like the House-passed bill, beneficiaries would be ineligible for Pell grants and must be able to read, write and speak English. Those stipulations were added last year to attract support from Republicans, most of whom characterize the DREAM Act as an amnesty bill that rewards those who broke the law when they entered the country.