A bill to provide $4.5 billion in emergency funding for the escalating humanitarian crisis at the border was on the rocks Tuesday as the White House threatened to veto over restrictions that would “hamstring” immigration enforcement — and liberal Democrats complained the bill did not go far enough to rein in the administration’s efforts on that front. Both the House and the Senate are scrambling to vote on funding ahead of the July 4 recess, amid reports of poor living conditions in government shelters and even deaths of child migrants as growing migrant flows flood across the border. More than 144,000 migrants were encountered or  apprehended at the border in May, many of them unaccompanied minors or family units, severely complicating efforts to house or deport them. The Department of Homeland Security (DHS) says the money to address humanitarian concerns at the border and in detention facilities runs out at the end of the month.