This helps explain why Cornyn skipped town in frustration yesterday after the two sides missed a deadline for a final agreement. He’s not just trying to drive a hard bargain with Democrats. He’s trying to perform for his Republican colleagues, who’ll one day be asked to choose a successor to Mitch McConnell and will want to know that he’s not a soft touch when negotiating with the other party.

He got an earful from conservatives during the caucus lunch a few days ago, Axios reports. Where’s the bill, they asked him? What, precisely, has he agreed to? Why are they intent on holding a vote next week instead of taking their time over the July 4 recess? Why have they focused solely on keeping crazy people away from guns and not on gun violence in cities like Chicago?

Figures like Mike Lee, Ted Cruz, Rand Paul, and Josh Hawley have been holding their fire publicly this week as a courtesy to Cornyn, to give him a chance to deliver something before they attack. One senses that ceasefire is about to end. It’s anyone’s guess whether the coalition of 10 Republicans who support the framework will hold once Cruz and the rest are on Tucker every night pronouncing federal money for state red-flag laws the greatest betrayal of individual liberty since slavery.

Several senators feel they’ve been shut out of the negotiating process and kept in the dark about crucial details, and will be asked to take a politically tough vote without enough time to digest the bill.

One GOP senator, speaking to Axios on the condition of anonymity to be candid about his concerns, branded Cornyn’s approach: “Shut up, and vote.”

“There’s considerable unhappiness in the conference that we seem to be approaching a bill that will unite all the Democrats and divide the Republicans,” said another senior Republican with direct knowledge of the internal talks.

The senior Republican mentioned that Sen. John Kennedy (R-La.) asked Cornyn during one lunch, “Are we focusing on gang violence and inner-city murders? And the response was, ‘No, we’re not focusing on that’ … And more than a few of us wondered why the hell not?”

The hasty timetable is an especially sore spot, although it may have less to do with conservative senators not being given enough time to read the legislation than not being given enough time to galvanize a grassroots push to kill the bill no matter what ends up being in it. But the slower Cornyn moves, the more nervous Dems get. “Democrats privately aren’t convinced yet that Cornyn is willing to reach a final agreement,” Punchbowl reports today, claiming “serious doubts” have arisen as to whether the deal will hold. “Democrats are eager to wrap up talks quickly – immediately – in order to get a bill moving toward the floor before the July 4 recess. If the negotiations drag on much beyond that, Democrats aren’t sure that it will ever happen.”

Conservatives are reportedly also worried that the 10 Republicans who support the deal will join with Democrats in voting down amendments offered by the right. Well … yes, that’s typically how bipartisan agreements work. Whenever the two sides try to get together on contentious legislation (immigration, most famously), the ideologues in each caucus scramble to push poison pill amendments which they know will amount to dealbreakers if they’re adopted. If Cornyn’s serious about passing this, he and the other nine GOPers may have to vote no on, say, a Mike Lee amendment to drastically increase due process protections before a state red-flag order can issue. Democrats won’t go for that for fear the amendment will make it practically impossible for such orders to be granted. Cornyn and the rest will have to grit their teeth and stick with the left.

But if it’s any consolation, that cuts both ways. One obvious amendment from the left would be to attach a total ban on adults aged 18-21 from purchasing AR-15s. That’s a nonstarter for Cornyn, although not for all Republicans. He’ll expect Chris Murphy, Kyrsten Sinema, and other parties to the deal to help defeat that amendment in the name of preserving the deal as-is.

Meanwhile, Republican pollster Neil Newhouse has been conducting private surveys to see where Americans stand on the deal, particularly Americans who own guns. Verdict: They like it.

We were contracted by [the conservative nonprofit] Common Sense Leadership Fund. There’s a lot of noise on this issue. We did this project to try to cut through what people really thought about guns — and specifically gun owners. We went into this with really no agenda. We simply wanted to test different alternatives, and specifically try to test what was coming out of the Senate negotiations.

These results were pretty surprising. I’m a campaign guy. And in campaigns, [if] you have a 60, 65 percent issue — that’s kind of like the gold standard in political campaigns. It’s a pretty good issue to use. And we found that most if not all the policies we tested ended up in the 70s and 80s — and that, again, is with gun owners. It’s clear from the data that Republican primary voters, at the very least, are not going to punish Republican members for voting for this.

A Fox News poll published this week found 77 percent of gun owners support letting the police take guns away from those shown to be a danger to themselves or others and 81 percent supported a total ban on buying AR-15s for under-21s. Newhouse told WaPo that his data looks similar. Again, though, bear in mind that there’s been little pushback to the deal from gun-rights supporters in Congress as of yet; once the “kill the bill” campaign begins in earnest on Fox News, those numbers may shrink. Bear in mind too that Americans are prone to saying one thing about gun policy to pollsters and then doing another once they get in the voting booth. Cornyn’s deal may not be as popular as it seems.

Stay tuned. Exit question: Is Fox’s new poll of Texas showing Beto O’Rourke within five points of Greg Abbott just statistical noise or something more? One recent poll had O’Rourke trailing by 15. Maybe the Uvalde shooting has (temporarily) made Texans more willing to prefer the Democrat in polling, if only as a way to signal that they want Abbott and the state legislature to Do Something.