Sen. John Cornyn (R-Tex.) is the new minority whip in the U.S. Senate. Unfortunately for the GOP, he’ll have two fewer Republicans to keep track of due to a terrible 2012 election. In an extended conversation with me this morning, he candidly says that under-performing candidates did in the Republican candidates for Senate in many cases. “At least in Missouri, Indiana and North Dakota, if we had different candidates and ran better races,” he says those seats would have gone for the Republicans. As head of the Republican National Senatorial Committee, Cornyn wryly notes that some insurgent groups had a “pretty poor” record in picking candidates. “Todd Akin couldn’t raise money and shot himself in the foot.” Indeed, many Republicans have observed that another problematic candidate, Richard Mourdock, is a nice guy and solid conservative, but mistakenly thought he could outtalk anyone.

But Cornyn is quick to point out that there is no one explanation for the GOP troubles. He says Mitt Romney is a “very nice man” who had vulnerabilities “exploited masterfully” by the Obama team. He returns to a common theme again and again. “The overarching way [to win in the future] is to show Republicans care about people like you,” he says referring to the broad spectrum of voters.

He’s also a seasoned politician and is forthright in saying that the GOP pollsters made a fundamental error in assuming a less Democratic electorate. He also says the GOP ground game must improve. Referring to the defective Romney get-out-the-vote program, he says, “Orca was symptomatic of the problem.” He, nevertheless, has confidence that the current Republican National Committee chief Reince Priebus is on the right track in his top-to-bottom audit of the election operation. “Reince is a very impressive guy. He started with a destroyed Republican Party.”

As the whip,Cornyn will be called on to round up votes on critical issues. Sen. Harry Reid (D-Nev.) is planning another assault on the filibuster. Cornyn says wryly, “When we do it, it is called the ‘nuclear option.’ When Democrats do it, it is the ‘constitutional option.’ ” He doesn’t think the assault will go anywhere, citing a news report that Reid has only 40-42 votes to change the rules. He recognizes that the GOP will have to articulate why it is important to preserve minority rights in the Senate.

He contends that by limiting amendments and cutting off debate, it is Reid who “has changed the nature of the institution.” He concedes that voters will “glaze over” if the argument is about arcane procedure. He suggests Republicans need to make the case that by curtailing the filibuster Democrats would be altering the checks and balances inherent in the system, and they need to remind voters that when the Democrats enjoyed one-party rule and pushed through legislation without adequate deliberation, the nation wound up with Obamacare. Indeed, he remarks, “The voters don’t trust anybody to have all the power. We still have divided government.”

His main focus is now on the fiscal cliff. He is wary of Republicans bidding against themselves. “The GOP says, ‘We’ll come up with more revenue.’ The Democrats say, ‘Fine . . . and we’ll take higher marginal tax rates, too.’ ” He is most critical of President Obama, who never has publicly put a grand bargain or complete tax reform or meaningful entitlement reform on the table. He concedes, “Part of it is our fault in not taking it to the president. The president for four years has basically had no plan.”

Cornyn wants to see presidential leadership (“Obama doesn’t want to get his hands dirty and roll up his sleeves”), while the president wants Republicans to “do the math” to see the purported need for tax rate hikes. Cornyn is blunt: “We’ve got to do the math.” Armed with concrete numbers about the revenue that can be raised from tax reform and the damage that would be done by letting the Bush tax cuts expire, Cornyn says it will then be up to Republicans to “penetrate” the media din and explain their position to the voters. “Republicans have not done a decent enough job,” he acknowledges.

He also chides the Democrats, especially Sen. Patty Murray (D-Wash.), for seemingly cheering a fall over the fiscal cliff. “It is beyond comprehension. No one could that irresponsible,” he says of Republicans’ aversion to allowing that to happen. He, nevertheless, thinks that pressure from the markets and from Democrats who will be up for reelection in 2014 “without the cover of President Obama” on the ballot will, with the usual brinkmanship, result in a deal.

He is less optimistic on sequestration. He agrees with Defense Secretary Leon Panetta that the cuts would be “devastating” but fears that the Democrats will be content to allow the massive cuts to defense to go forward rather than negotiate an alternative set of cuts. The only alternative Cornyn thinks Democrats would accept is a complete rescission of sequestration (thereby sparing domestic cuts).

As for the new Senate, Cornyn notes that moderate Democrats and moderate Republicans will be leaving the Senate. “We will have a more conservative group. Democrats will have a more liberal group.” That may help Republicans internally stick together, but he is fully aware that Democrats will try to peel off Republicans on key votes.

On the hot-button issue of immigration reform, Senate Republicans are in a tough spot. Even if they show political courage and can cobble together a plan, they risk being undercut by the Republican House, which could well kill legislation.

Most eyes have been on Sen. Marco Rubio (R-Fla.), but Cornyn and others (even Sen. Rand Paul [R-Ky.]) may be better-suited to carry the ball. Cornyn says, “I come from the perspective of my state. We’re a third Hispanic.” He call it a “demographic necessity” for Republicans to expand their appeal with Hispanics. (In a specific criticism of Romney, he notes, “He got pushed to the right on immigration in the primary and never made it back.”) He says immigration reform is not a cure-all for Republicans. He cautions that in courting Hispanics, “The first thing you have to do is show up. You have to demonstrate respect.” And he points to education, social issues and pro-business policies as other issues that Republicans should be using to expand their appeal.

But he comes back to the tone and the substance of immigration policy. He visibly recoils when he repeats some of the catch-phrases that turn off Hispanics — “self-deportation” or “attrition.” He is optimistic that with border security and work-site enforcement there should be a “straightforward solution” to dealing with the 12 million undocumented immigrants already in the country. He recalls that in 2005 he and Sen. Jon Kyl (R-Ariz.) introduced an immigration bill that “still looks pretty good.” He says matter of factly of the prospects for immigration reform, ”A lot of work has been done on this. We know what the range of choices are we need to find a way to advance it.”

Cornyn has sometimes been the subject of ire from right-wing pundits and tea party organizers. But his style of pragmatic, less angry Republicanism may be in fashion — and a necessity — if Republicans are to carve a new agenda, repair their electoral shortcomings and be positioned in 2014 to regain seats. As for 2016, Cornyn groans. “I dread talking about 2016.” Indeed, there is plenty to be done before a number of his Senate colleagues start posturing and preening for a presidential run.