One way that the Democratic Party can prevent a loss of the Massachusetts Senate seat from stopping their healthcare program from becoming law, without either reopening negotiations (e.g. trying to get one of the Maine Republicans to vote with them) or using hardball tactics (e.g. finding a procedure to pass the bill without needing 60 votes), is for the House simply to adopt the Senate bill. Then it would not require another vote in the Senate.
Would the House do that?