WASHINGTON – When President Donald Trump climbs the rostrum to deliver his second State of the Union address, he'll share the stage with the Democrat who has become his most vexing political rival: House Speaker Nancy Pelosi.

White House aides say Trump intends to deliver a speech focused on bipartisanship. But sitting just over his left shoulder in the House chamber, the California Democrat will be a stark reminder of the precarious state of his proposed border wall, the negotiations to avoid another government shutdown and his legislative agenda for the next two years.

Associates of Pelosi and Trump said the president appears to have initially misread the speaker and underestimated her willingness to stand firm against his demands for money to pay for a border wall. Trump ultimately agreed to temporarily end a 35-day government shutdown last month even though the short-term funding bill included no money for his border wall.

Earlier, the two clashed about the timing of Trump's address. After Pelosi suggested the president wait to deliver the State of the Union until after the government reopened, Trump first threatened to deliver the speech in another venue before he relented and agreed to hold off until Tuesday.

“I think she’s trying to prove that controlling the House allows her to dominate the outcome,” former House Speaker Newt Gingrich, a Trump ally, told USA TODAY. “And he’s trying to prove that being president allows him to define the outcome. And they have very, very dramatic different goals in mind.”

Trump had demanded $5.7 billion to build a wall along the U.S.-Mexico border to end the government shutdown that had dragged on for more than a month, leaving some 800,000 federal employees without a paycheck. Democrats refused to allocate the money, and Pelosi called a wall “immoral.”

"This is the first couple of rounds of a long heavyweight battle. I think they’re both trying to see what punches land and how their opposite member reacts," said Mark Harkins, a senior fellow at the Government Affairs Institute at Georgetown University.

Not her 'first rodeo'

Harkins predicted that strategy would favor Pelosi.

"The one with more experience probably knows more about what they’re doing. This is not Speaker Pelosi’s first rodeo," Harkins said.

Neither Pelosi's office nor the White House responded to questions about the relationship, but analysts said the cold shoulder was predictable. Republicans have turned Pelosi into a bogeyman representing the liberal wing of her party for more than a decade.

In that sense, the relationship has been notable for the fact that Trump has been less personally critical of Pelosi. He has not, for instance, tagged her with a nickname as he has other political opponents. Trump calls Senate Democratic leader Charles Schumer "Cryin’ Chuck" but acknowledged this week that he likes to call Pelosi, simply, “Nancy.”

“I think about it in terms of two people who may not have any incentive to work with each other,” said Scott Jennings, a GOP consultant with close ties to Senate Majority Leader Mitch McConnell. “It doesn’t portend for a lot of cooperation over the next years.”

Jennings said he believes the White House badly misread Pelosi immediately after the November midterm election, as indicated by Trump's repeated predictions that the then-incoming House speaker would be more likely to make a deal after she assumed power.

"'Misreading' is a charitable word," Jennings said.

Trump and Pelosi have ramped up their rhetoric in recent days. The president, in an interview with CBS, described Pelosi as "very rigid" in talks with the White House leading up to the shutdown. He has claimed that she "wants open borders" and "doesn't mind human trafficking."

Pelosi and others have questioned the effectiveness of Trump's wall and have described Trump's remarks as "wild and predictable misrepresentations."

Kinder, gentler speaker?

Rep. Mark Meadows of North Carolina, a conservative Republican who is close to the president, said that in private, Trump's opinion of Pelosi "has always been one of a worthy adversary."

"I don’t think he’s underestimated her," Meadows said. "I think he was getting advice from people on Capitol Hill, and some of his advisers, that she would be a kinder, gentler speaker as it relates to issues where they disagree. And I think that was misplaced advice."

House Democratic Caucus chair Hakeem Jeffries, D-N.Y., said Trump "may have underestimated her in the weeks leading up to Democrats taking back the majority," but after watching her in action, "no one should underestimate" her.

Trump and Pelosi did not speak for weeks during the shutdown. The two spoke by phone on Jan. 28 to confirm details of the State of the Union.

Conflict between presidents and House speakers from opposing parties are not new. Pelosi sparred with President George W. Bush the first time she was speaker, at one point calling him "a total failure." But Pelosi told USA TODAY in December she was nostalgic for the former GOP president because when negotiating, "we started with a stipulation of fact." She said that baseline does not exist with Trump.

Gingrich, who was speaker during the second longest shutdown on record, under President Bill Clinton, said Trump and Pelosi are so far apart, it's hard to see how they'll ever compromise.

“Clinton and I were not that far apart – he’d run as a centrist Democrat," Gingrich said.

"There were a lot of places where we could find a common ground. It’s much harder, it seems to me, dealing with Pelosi, to imagine any kind of common ground."

The mutual mistrust could hamper progress on policies where there had long been some hope for bipartisanship, such as on reducing the price of prescription drugs or increasing federal spending on infrastructure.

“I don’t think the shutdown impasse completely precludes working together on an issue of mutual concern in the future,” said longtime GOP strategist Michael DuHaime. “But it certainly doesn’t look like this relationship will ever be confused with Ronald Reagan and Tip O’Neill finding compromise."

More:Exclusive: Nancy Pelosi vows 'different world' for Trump, no more 'rubber stamp' in new Congress

More:In Trump era, Nancy Pelosi admits to nostalgia about George W. Bush. Here's why