President Obama is right to pull out troops if Karzai doesn't sign an agreement. We are keeping him in power and he treats his protectors like crap. If he doesn't sign an agreement, I wish him good luck, because he will surely need it to stay in power without our muscle behind him.
The debate question asks something that is overly specific. It is acceptable for President Obama to withdraw troops from Afghanistan in these specific circumstances (if Karzai won't sign the agreement to keep troops in place) because it is acceptable to remove the troops from Afganistan in all circumstances. The war in Afghanistan has been costly in blood and treasure, and the only thing gained was the death of Osama bin Laden. The country is in worse shape than it was when the Americans arrived, and the Taliban are not destroyed. Both parties would be better served by the removal of American troops, regardless of whether or not Karzai signs the agreement.
It would be important for Obama to be engaging with other countries diplomatically, and especially in a situation where troop presence is occuring it is important to have consent from all involved parties. It the troops are not wanted there or certain agreements aren't met, they should be pulled out.
I think it is completely acceptable. For a large part, the troops are there to help support Karzai and his government, and to help keep them in power. The US government is entitled to expect Karzai to co-operate with the US. If Karzai refuses to sign the agreement, then the US is entitled to do with its troops what it wishes, including pulling them out.
I believe it is acceptable for Obama to say that troops will be leaving Afghanistan if Karzai doesn't sign the agreement to keep the troops in place. I don't really consider this a threat, it's simply a matter of fact. As the acting president, Karzai can decide to keep the troops, but if he doesn't sign then that's a clear indication they aren't wanted there and we should leave.