Graham is getting praised by conservatives for this proposal, which was the subject of the Tuesday hearing that called for McAleenan's testimony. The legislation is, in fact, basically the bill version of the Trump administration's wish list for dealing with what many consider an escalating humanitarian crisis.
It's also another way of scoring political points back home. It shows he's loyal to President Donald Trump, and it's also in keeping with the new, ultra-conservative reputation he has cemented for himself since his defense last fall of embattled Supreme Court Justice Brett Kavanaugh.
That move endeared Graham to Trump's base and was followed by high marks in public opinion polls -- a far cry from the calls of "Grahamnesty" the senator endured when he was pushing the 2013 immigration proposal.
By continuing to bring up his old immigration bill, Graham could undermine the developments that have so far inoculated him against primary challengers ahead of his bid for reelection in 2020.
But Graham, whose default position as a legislator is that of a dealmaker, is eager to find a compromise that allows his bill to advance. He plans to schedule a Judiciary Committee meeting for next week to debate and make amendments to the measure, and has invited Democrats to offer their policy suggestions.
He's optimistic Democrats are realizing they'll be blamed politically for stonewalling a bill to stem the border crisis, just as Republicans will be blamed if they can't send their president a bill that addresses the dilemma because of a refusal to negotiate.
"If they don't get the reality that we're working in good faith with them and they say 'no,' they're going to get blamed," Graham predicted, "and vice versa."
There's another political advantage for Graham in proceeding on this path: He could end up presiding over a bipartisan compromise bill that gets signed into law by a Republican president who still remains popular in his state.
The chances for such an outcome are slim given the partisan acrimony and distrust around the immigration debate particularly. Even Graham has signaled some equivocation on how committed he is to bipartisanship this time around, suggesting just weeks ago he would only let Democrats debate broader immigration legislation if they agreed to pass his asylum bill first.
Still, there were signs of a thawing of partisanship at the Judiciary Committee hearing on Tuesday.
U.S. Sen. Dick Durbin, D-Ill., Graham's longtime partner on immigration legislation, said he could not support the border security bill as written, but that he was "hopeful" members of both parties could find common ground.
"I'm hopeful because I know this chairman," Durbin said. "I've worked with this chairman on bipartisan solutions."
"I hope, Mr. Chairman, that your side will sit down with us and see if we can't work out some bill of which we, as Americans, can really be proud," U.S. Sen. Dianne Feinstein of California, the top Democrat on the Judiciary Committee, added.
(c)2019 McClatchy Washington Bureau
Visit the McClatchy Washington Bureau at www.mcclatchydc.com
Distributed by Tribune Content Agency, LLC.