I don't think the Senate needs to go along. The House holds the purse strings.
That is my understanding anyway.
The reason the House is considered to hold the purse strings, is because any spending bill is required by the constitution to originate in the house. But the Senate still has to go along as well as the President before any spending bill becomes law. Unless of course the President's veto is overridden and then the President doesn't matter.
Likewise, any bill to defund, would also need the Senate's approval as well as the President's signature or a veto override.
The vote clearly lets the President know that the House doesn't approve of his dream act executive order. But without the Senate it's nothing more than a nice strongly worded letter.
And I'm still confused about what it means to defund non-enforcement of the law.