You can count on an anti-2nd amendment cabinet that is for certain. You can probably count on some serious rhetoric from Feinstein, Pelosi, Kerry, and company. I have no doubt HR 1022 will be dropped again, under a different number, but language nearly identical or even more restricting.
That said Heller, while not going as far as some would have liked, was in no way a victory for anti-2nd amendmenters. The NRA and gun lobby gained a lot of political capitol with the Heller decision and they are starting the process of taking on other cities, Chicago being one. Additional decisions in favor of 2nd Amendment rights which cite Heller as precedent will only strengthen the constitutional grounds for personal gun ownership. That said, should something like HR 1022 pass you could sue the government over each gun, but you could also sue over the entire act, take it the SCOTUS and potentially win. If done before Obama has an opportunity to nominate a justice the case would likely fall in favor or the 2nd.
Current political theory suggests that because SCOTUS historically has the highest approval rating (well above 50% with 48% being a 'historic low') the public usually trusts the court to make the right decision and supports that decision once its made. Essentially that the SCOTUS influences public opinion and in turn public opinion influences the court. I personally dont think that public opinion supports an over arching gun ban as described by HR 1022. Remember that gun control was not a huge part of the debate during the election, likely because of the Heller verdict and because people want 'change' in areas other than gun control.
Additionally a lot of House Democrats and Senate Democrats won by slim margins in battle ground areas. Especially in the House freshman Democrats coming from moderate constituencies might not have the political capitol to vote for such an extensive ban. That could work in favor of 2nd amendment rights.