Trump did not specify what he meant by strong border security. However, he has in recent months called for tough restrictions on legal immigration in exchange for shielding the young immigrants. Democrats and numerous Republicans do not support the proposed limits on legal immigration, which include restrictions on family visa sponsorship and an end to the diversity visa "lottery" system.
The president's mention of a "real" border wall may allude to his frustration with a $1.3 trillion spending bill he reluctantly signed into law earlier this year. While the measure increased border security funding by $1.6 billion, the money largely went to surveillance technology and border fencing similar to structures that already exist, rather than a "wall" as Trump conceived it.
Senate Majority Leader Mitch McConnell on Thursday also shot down the prospect of approving an immigration measure the president does not support. In an interview with The Wall Street Journal, the Kentucky Republican said senators cannot "spin our wheels" like they did in February, when an open amendment process yielded multiple failed immigration proposals.
"If the House passed a bill that the president was for—in other words I thought there was a chance of actually making a law—I'd consider it," he told the newspaper.
Immigration policy has confounded and divided Congress for years. Finding a solution for the young undocumented immigrants, known as Dreamers, took on more urgency when Trump ended the Obama-era Deferred Action for Childhood Arrivals last year.
While court decisions have held up his move, many lawmakers seek a quick resolution to end the uncertainty. But earlier this year, lawmakers could not reach a consensus as Trump's demands for a bill appeared to shift.
The centrist Republican effort has thrown chaos into the GOP caucus only months ahead of elections that will decide whether Republicans keep control of the House. Last week, the House Freedom Caucus, failing to secure a vote on a conservative immigration bill as support for the moderates' plan mounted, helped to sink a GOP-written farm bill.
The immigration fight has multiple political implications for Republicans. Discontent has grown with Ryan, sparking speculation about whether lawmakers could try to force him out before his planned retirement in January, according to Politico. House Majority Leader Kevin McCarthy, Ryan's handpicked successor as House GOP leader, also cannot run afoul of too many members and still win a leadership race.
McCarthy believes reaching a bipartisan immigration plan with Democrats could hurt Republican voter enthusiasm in November, according to Politico.
On Wednesday, the House Republican conference confirmed it will hold a two-hour meeting next month on immigration. Lawmakers could potentially forge a path forward then.