Trump's demands for funds to build a border wall, which prompted the 35-day government shutdown that ended late last month, are not the central sticking point in the current impasse.
Instead, the two sides are at odds over Democrats' attempt to impose a new cap on detentions of immigrants apprehended within the US - as opposed to at the border.
Republicans want to exclude immigrants charged with or convicted of certain crimes from the cap, arguing US Immigration and Customs Enforcement might not otherwise have the ability to detain dangerous criminals. Democrats say excluding people from the cap would render it toothless, as they seek to rein in the Trump Administration's aggressive enforcement policies.
Trump Administration officials said yesterday that that the chances of another government shutdown had increased markedly over the weekend. White House counsellor Kellyanne Conway said Democrats' demands were to blame for the renewed risk of a shutdown.
"The President is not a part of these negotiations. He's waiting for a bill to come to his desk that he can sign into law," she said on Fox News Channel. Democrats are "the ones hurtling us toward a shutdown," Conway said.
Lawmakers frequently run up against deadlines to pass spending bills, but it's unclear whether they can rely on the most commonly used fallback plans this time. Often, lawmakers will seek to pass short-term spending bills that last for several weeks in order to buy more time for negotiations. But they have already done that several times in recent months, and it's uncertain whether they would take that step again.
Trump has readied a plan to declare a national emergency on the southern border, which he believes will allow him to redirect taxpayer money from other projects in order to build parts of a wall - without approval from Congress.
White House officials have said they would give the current negotiations a chance to succeed before moving forward with their plan, but they haven't revealed an openness to delaying any longer.
The meeting comes at a pivotal time. Trump plans to travel to El Paso for a rally today, and is expected to restate his case for tougher immigration rules. Republicans in Congress have tried to avoid Trump's hardline rhetoric during negotiations, but his support is crucial for a final deal.
The President on Twitter alleged Democrats are trying to create new protections for undocumented immigrants with criminal records.
"The Democrats do not want us to detain, or send back, criminal aliens! This is a brand new demand. Crazy!" he wrote.
But Democrats have said this mischaracterises their position. They said the White House's insistence on excluding people charged or convicted of crimes, even nonviolent drug offences, would give the White House almost limitless power to detain people and make existing rules irrelevant.
