After having his State of the Union address temporarily canceled during the government shutdown last month by House Speaker Nancy Pelosi, President Trump Tuesday will finally take the greatest stage in politics to make his case for a wall on the Mexican border.

“It's one of the few times, like the Super Bowl, where you have all the American people watching, and if you handle it in the right way, you can move the voters,” said former Senate Majority Leader Trent Lott, R-Miss., who attended more than 30 State of the Union addresses during his time in the Senate and the House.

“The danger will be if he gets off script, or if the Congress acts like a bunch of imbeciles, which we quite often do,” Lott said.

White House officials teasing the speech have emphasized a bipartisan message while also saying Trump will push his signature 2016 campaign promise of a wall. House and Senate Democratic leaders have refused to fund either a wall or steel-slat barrier, however. Trump will either try to galvanize public support for pressuring Democrats to agree to fund a wall, or for an emergency declaration he might make to build it unilaterally.

Pollster John Zogby said Trump faces a difficult task. “He really comes into this State of the Union with his back to the wall,” Zogby said, pun apparently not intended. “The wall is inextricably linked to the shutdown. And the shutdown did considerable damage to himself and to the GOP. They got the bulk of the blame and his numbers went down.”

Public support for the wall crossed 40 percent during the shutdown, but never neared a majority, Zogby said, though he found that emphasizing the underlying border security justification seemed to improve public opinion.

But Zogby added: "I think [House Speaker] Nancy Pelosi and [Senate Minority Leader] Chuck Schumer are flexing their muscles right now. What they saw was when push came to shove with the shutdown, they came out winners, or at least not the big losers.”

The federal government careened into a 35-day government shutdown before Christmas when Trump responded to a brewing rebellion among his base by declaring he would only sign a large spending bill with wall funds. As the shutdown progressed, Trump floated declaring a national emergency to build the wall if Democrats did not support it.

A senior administration official briefing reporters on Friday would not say if Trump will announce an emergency declaration during the speech. Trump suggested to reporters last week that he might.

“Obviously this is as much a pitch to the American public as it is to congressional Democrats,” said Ira Mehlman, media director of the Federation for American Immigration Reform, which seeks to reduce immigration.

“There are Democrats who support this and are willing to consider border wall funding,” Mehlman said, indicating he's still hopeful that ongoing bipartisan negotiations for funding a wall — which could obviate the need for an emergency declaration — will lead to a breakthrough. “The polls have indicated Americans understand the need for real border security," he said.

But potential olive branches risk alienating Trump's base. Mehlman opposes an offer to expand protection for young illegal immigrants as part of a deal, though Lott endorses the idea, saying Trump should show flexibility.

Lott, the former Senate majority leader, added, "I've never been a big fan of the wall. In my farm in Mississippi we have goats and we just about can't fence them in, or fence them out. I think people are just as smart as goats.”

[Read more: 'A WALL is a WALL': Trump mocks Congress for talking about fences, barriers]

At the same time, Lott said he believes a wall in some parts of the border would make sense, combined with other border security technologies.

But if Trump uses the speech to try to convince Democrats to support wall funding and it doesn't move Democratic votes, Lott said, "I would declare a national emergency. I would move the Seabees and the Corps down there and build an obstruction that a Mack truck couldn't get through."