I doubt that a majority of the Senate would sign it, as political demographics currently stand. Even most Democrat voters are now in favor of the Second Amendment.
IMO, favorable, pro-Second-Amendment political conditions will continue, as long as imports and sales of cheap, semi-automatic rifles favored mostly (not all) by slum dwellers and other lefties continue. Not knocking AK variants here, but defending imports (including cheap ammunition) is something to think about for political public affairs.
If vendors tighten-up, price up or are outlawed on those kinds of imports and sales, then watch out. More Democrat and many Republican voters will turn back to favor anti-Second-Amendment laws sooner. Remember the year that the AWB was passed and who was in political offices.