Inasmuch as President of the United States (US) Donald Trump has quipped that the shutdown of the federal government could last for a very long time because he apparently, has no intention to budge from a demand for $5 billion to wall out Latinos at the US southern border, the reality of Trump's political survival suggests that he'll be severely weakened going into the State of the Union address on January 29, 2019, having the federal government shuttered.
Trump is set to deliver the annual State of the Union address before the chamber of the US House of Representatives on January 29. This yearly rite of presidents has been conducted to attest to the good health and strength of the Republic. It would be a farce for any sitting president with a shuttered federal government to declare that the State of the Union is "good".
Mindful of this, and having dreams of 2020, Trump will likely do whatever he can to end the shutdown before January 29. While Democrats are unlikely to cave in to Trump's demand for a wall and that Trump's ego stands in his way to reopen the government without a Mexican border wall, expect Trump to declare a national emergency to get his wall, thus allowing for government workers to return by January 29.
Therefore, even though Trump is often unpredictable, I venture here to suggest that the government shutdown should be over by January 29.