1. The Senate failed to pass two competing proposals to reopen the government, sending lawmakers back to the drawing board for a bipartisan solution to end the impasse.

The Republican proposal included $5.7 billion in funding for President Trump’s border wall, paired with legal protections for some immigrants. The Democratic proposal would have temporarily reopened the government until Feb. 8, but it omitted wall funding. A half dozen Republicans voted for it, but the tally still fell short of the 60 votes it needed to advance.

Lawmakers and aides in both parties expressed hope that the double-barreled losses would break the logjam that has gripped Washington since the partial shutdown began. House Democrats said they were considering giving Mr. Trump as much as $5.2 billion for border security — but not for a wall.