Yes they can cut the funding in the next Budget, and if they do then Obama will Veto the Budget and if congress keeps submitting a Budget to Obama with Funding for that or for Obamacare cut and Obama keeps vetoing it the Government will shut down.

What I hope is Congress has the balls to refuse to remove the Funding Cut and does not back down even if the it takes to the general Election to have a Budget.

Congress can always tell the People that if Republicans had a Veto Proof Majority or a Republican President then there would be a Budget.