The White House has the ability to shame congress into action. Stage a series of press conferences and meetings with Congressional leaders. Publicly twist arms. If they wot meet, launch a press conference about that. Issue Executive Orders. Make it a Republican obstructionist media story.
There's so much the President ca do to restore EUC benefits and so far he's chosen to be passive.
Not only will an aggressive high pressure campaign help 3 million American families, it will drive Republicans out of seats for turning their backs on America.