Rep. Mike Doyle (D-PA) introduced a discharge petition allowing the House to force a vote if half of the representatives sign on -- an action to get around the Speaker of the House Paul Ryan, who would almost certainly stall a traditionally-presented motion to save net neutrality. This is still an early move in a long campaign, however, as Democrats would need to conceivably convert more than a score of Republicans in the actual House vote.
Given that the Senate vote tracked along party lines, except for the three Republicans, representing 3 percent of that chamber, it will take more convincing to convert five percent of the House. Per the Electronic Frontier Foundation, 160 representatives have pre-committed to voting for the bill if it should reach the House floor. But it could take some time to gather all the signatures.
If a net neutrality-saving resolution did somehow pass, it would head to Trump's desk and a very likely veto. But for advocates of an accessible internet free from throttling by service providers, this is a necessary and encouraging step. Democrats are attempting to stop the repeal of net neutrality rules passed in 2015 which essentially prevent internet service providers from arbitrarily restricting or slowing access to websites.