The threat on negotiations over the Obama-era program known as the Deferred Action for Childhood Arrivals, or DACA, comes as the Senate holds a rare open-ended debate on immigration. Mr. Trump ended the program in September, giving lawmakers until March 5 to agree on a replacement so that about 700,000 young immigrants are not deported. That deadline, however, is not as firm as the president suggests. A federal judge in California ordered the Trump administration to restart the program last month.