How did Southern German nationalistic fervor solve Bismarck's problems with the Prussian parliament? Simply by distracting them with "good news"?
Problem is that a South German Bund would be dominated by Bavaria - and Protestant Badeners and Wurttembergers would dislike domination by Catholic Bavaria even more than by Protestant Prussia.
It was about seven weeks from the French DoW to the surrender at Sedan. That aroused enough enthusiasm to ensure that unification would go through.
First of all, it would not just mean a South German nationalistic fervor. The nationalists were actually stronger in western and northern Germany, while in southern Germany they were certainly present and quite vociferous but the conservative and localistic interests were a majority. Then there is the problem of Prussia (which accounted for 80% of the population of the NCG): while the nationalists were also present in Prussia, they were more concentrated in the west: Brandenburg and Prussia proper were more tepid about a full merger of Prussia into a pan-German state (which as a matter of fact did not happen IOTL when the Reich was proclaimed). This was mirrored by the actual distaste of traditional German states who feared to become mere Prussian appendices.
Bismarck had two main worries: the cost of a prolonged war (which would have to be borne mainly by Prussia alone and would create significant issues in the Prussian parliament) and the danger of involvement by the other European powers which became more and more real with an extended duration of the war: Prussia had substantially enlarged its territory after the war of 1866 (straight annexations, as well as the Prussian-dominated NCG) and had tied up the South German states with the defense treaty provisions and their participation in the Zollverein (the Zollverein as reformed after 1866 gave Prussia the right to dissolve the Zollverein with a 6-month notice and Bismarck was not shy in using this threat against Bavaria in particular). The disastrous French position after Sedan, in the view of the European Powers, raised the danger of a Prussian annexation of Northern France (not a realistic fear, but perception is master) or the risk of a revolution in France: neither of these outcomes would have been acceptable. The failure of diplomatic talks in St. Petersburg in late 1870 (mostly due to British reluctance in taking firm commitments) lessened the risk of international intervention (at least for the time being) but did nothing to ease Bismarck's budgetary worries.
There are reasons for Bismarck to curse the French emperor, not just for his mad idea of relieving Metz but even more for allowing himself to be captured after Sedan: the chance of an early close to the war disappeared at a stroke.
Starting in November, Bismarck had to accept to play the nationalistic card once more, to use the nationalistic votes in the Prussian and NCG parliaments to curb the resistance of Prussian conservatives to new taxes. The path he chose was to woo Bavaria (with promises, threats and a golden handshake) and by end of December the Bavarians were on board: the imperial crown was offered to the king of Prussia by the king of Bavaria, on behalf of the other German states. It was a long and costly negotiation, and Bismarck would have preferred not to need going through it.
Bismarck's preferred strategy would have to wrap up the war as soon as possible, and his plan with regards to the South German states was to induce them to form the South German Confederation: Bismarck thought that this junior confederation would have anyway be firmly tied in the Zollverein and the supra-national organization would have reduced over time the independent inclination of the southern states, make them more homogeneous and prepare them for the next step of being absorbed in the new German Confederation he planned. A German Reich was not really attractive to him, although I'm pretty sure that it figured as plan B of his strategy.