WASHINGTON — The Senate summarily blocked three measures on Thursday — including one backed by President Trump — to resolve the fate of the so-called Dreamers, leaving hundreds of thousands of them facing an uncertain future.

As senators struck down measure after measure, a week that began with the promise of a rare open, free-ranging debate on the issue crashed headlong into the same divisions that have prevented Congress from fixing the nation’s immigration system for decades. The lack of consensus left in question whether any solution on the Dreamers can be reached.

In a rebuke to the president, senators voted overwhelmingly, 39 to 60, against the White House-backed bill, which would have committed $25 billion for a wall along the border with Mexico, placed strict limits on legal immigration, ended the diversity visa lottery and offered 1.8 million Dreamers an eventual path to citizenship.

Senators were 21 votes short of the 60 required to open debate, and the rejection of the president’s plan was bipartisan: Democrats refused its get-tough approach to legal immigration, while many conservative Republicans derided it as amnesty.