If they ask you to enter the password there and contribute to its destruction or the destruction of its contents so as to obstruct an investigation, couldn't it invite charges of obstruction of justice or other charges?

TrueCrypt works well in terms of plausible deniability so as to mitigate risk of charges, but there are approaches that work better than any single one of the approaches mentioned here.

One approach is to combine the above mentioned approaches to make sure the key to decrypt is never in your possession when crossing the border.