The government of Teresa May, Britain's previous prime minister, was able to reach a deal with the European Union on the terms of the Brexit but Britain's parliament, which needs to approve the Brexit deal first, didn't.
In fact, what's called the " meaningful vote" on the deal was originally scheduled for December 11th but because it looked like parliament was going to reject it at that time, the vote was delayed until this Tuesday.
Even if the Senate joins the House and overturning the emergency declaration, President Trump would veto that and it would probably stand but there are other challenges.