Updated at 10:30 a.m. with additional comments from AT&T chief executive Randall Stephenson.

WASHINGTON — AT&T chief executive Randall Stephenson said onWednesday that Republicans' "political survival" may hinge on their ability to produce a major overhaul of the tax code that features a lower corporate rate.

The boss of the Dallas-based telecom giant offered that prod at a Business Roundtable panel discussion featuring several high-profile chief executives.

And Stephenson, who issued a broad call to action, applied the most direct challenge to the GOP, which controls the White House and both chambers of Congress. He said a failure to overhaul the tax system would "literally be a bad indictment" of the party's effectiveness.

"If you're a Republican, you better have it done before the primary season," he said. "Seriously."

Randall Stephenson, the chief executive of AT&T, said Republicans' "political survival" may hinge on whether they successfully overhaul the tax code. (Brandon Thibodeaux / The New York Times)

The heavyweight scold highlights the stakes of the tax debate as GOP leaders prepare to offer a more detailed proposal as early as next week.

Earlier Republican tax proposals have offered corporations a favorable outlook. Business leaders have continued to stress the need for a lower corporate rate and a move to a territorial system would tax U.S. companies only on their profits produced in the U.S.

And Stephenson and the leaders of Lockheed Martin, Boeing, EY and UPS on Wednesday all made the case that the time was ripe for Congress to act.

But for all that cheerleading, the specter of Washington gridlock nonetheless loomed over the gathering of top corporate minds. Asked if any of the companies had budgeted with a successful tax revamp in mind, Stephenson didn't hesitate.

"We wouldn't dream of it," he said.

Then David Abney of UPS jumped in.

"It's been 30-something years," he said, referring to the last time Congress overhauled the tax code. "Even though we are pushing real hard and we want to make sure it gets done, it's just too much uncertainty."

And then, finally, Marilynn Hewson of Lockheed Martin offered a more positive outlook.

"But we're optimistic," said Hewson, whose company makes the F-35 in Fort Worth.

The Business Roundtable, which organized the panel, is a Washington group that represents top corporate executives. And there was little doubt that Stephenson and his cohorts were aligned on their No. 1 priority in the tax debate: lower corporate rates.

The U.S. has one of the highest statutory corporate rates in the world, though many companies end up paying a lower effective rate thanks to various loopholes and deductions.

Stephenson said it was crucial to make the corporate tax rate more competitive by lowering it from its current 35 percent to something closer to 20 percent. And he said that means business leaders have to "figure out what we can live with to get this tax rate down."

One example came when the AT&T boss was asked if he would be OK with the top individual tax rate staying the same.

Stephenson said "there's a lot that's going to go into the sausage-making" of a major tax revamp. He added that he's a "bit ambivalent," given everything else at play, about the idea of keeping the rates on the wealthiest taxpayers the same.

But he said the end objective had to be an overhaul that allows business to invest more and create more jobs.

"Whatever happens beyond getting this corporate taxation competitive, if it gets us closer to that objective, then great, let's do it," he said.

Marillyn Hewson, president and CEO of Lockheed Martin Corp., said she remains optimistic that Congress will revamp the tax code. (Getty Images)

The CEO panel acknowledged that there could be other worthwhile tax proposals, such as lowering the tax rates for "pass-through" businesses that pay their taxes through their owners' personal returns. But Stephenson, in particular, turned time and again to the corporate rate.

He said that AT&T had run the numbers "nine ways to Sunday" and found that a successful revamp would cause the U.S. economy to grow at least a 3 percent rate. And he said it would push his company to "take our $22 billion a year we invest in American" and "step it up."

Each billion dollars in investment, he said, would lead to 7,000 "hard-hat jobs" putting fiber in the ground or building cell towers.

"It's a big deal for job creation," he said.