The FCC, based on past experience, will treat the petition exactly the same whether it has one signature or 10,000.

The US Senate is unlikely to pass a bill to overturn HOA's regardless of how many petitions are submitted. If a Senate solution is desired, first, you have to find a Senator willing to introduce the legislation... second, you have to hope that the Senator has the means or chutzpah to make sure that the proposed legislation doesn't die in committee... and third, you then have to convince at least 50 other senators to vote in favor of it.

One petition sent generically to the Senate as a body just ain't gonna cut it, bunky!