Yes, you have 60 days to complete an indirect rollover including a Roth conversion. For current tax purposes the distribution will be taxable in 2012 because the 1099R for the distribution would be a 2012 1099R.
HOWEVER, your conversion would actually be completed in 2013 and the Roth custodian will issue a 5498 showing a 2013 conversion contribution. For any 5 year holding requirement for this conversion, the 5 year period starts 1/1/2013, not 1/1/2012. This means that you have an extra year to wait to avoid the 10% penalty if you need to withdraw the conversion from the Roth IRA before age 59.5. And if this conversion is your first Roth contribution of any type, the 5 year holding period for the Roth to become qualified (along with reaching 59.5), will also start in 2013 instead of 2012.
Regular Roth contributions can be made as late as 4/15 for the prior year, but conversions are not eligible for this and follow the above rules.