If Trump thinks he has public support for his shutdown of the government, he is sadly mistaken. Poll after poll has shown the public doesn't want his silly wall, is upset the government has been shutdown, and blames Trump for the shutdown. His job approval is shrinking. And it's his own fault. He is trapped, and it's a trap of his own making. His position is getting weaker by the day, and threatens to derail the last two years of his term.
Here is some of how Jennifer Rubin describes Trump's dilemma in The Washington Post:
The irony here — or is it karma? — is that Trump’s biggest cheerleaders in the right-wing media (e.g. Rush Limbaugh, Sean Hannity) and his hardcore anti-immigrant adviser Stephen Miller who egged him on are now responsible for the worst political debacle of his presidency, one that has erased any residue of presidential power. He’s now trapped, waiting for a permission slip from the right-wing media chorus to capitulate — or watch his support and any hope for legislative accomplishments evaporate. As to the remainder of his term, Trump was never going to advance any proposal on a wide range of issues without Democratic-buy in. Now, having empowered them and weakened his own hand, he’ll either have to give more ground in future negotiations or meekly accept two years without a significant accomplishment. For now, his agenda is on hold. (“The standoff has already forced Mr. Trump to cancel a trip to Europe to meet with global business leaders in Davos, Switzerland, at a time when the world economy faces a possible slowdown,” the New York Times reports. “The president has made no evident progress in filling a series of senior vacancies nor has he produced the tax-cutting plan he promised last year. He has done nothing in weeks to publicly promote priorities like fighting opioid abuse or bolstering the economy.”) Trump cannot bear to face the possibility of defeat on the issue that was most central to his campaign and most closely tied to his theme of white grievance. As with trade, however, his fixation with avoiding defeat leads to further erosion of his power. He faces a lose-lose choice: Give in now, as humiliating as that might be, or alternatively, continue a fruitless fight that will sap his chances of political survival and still not avoid eventual defeat.