The original conversion from a Traditional IRA to a Roth IRA must be completed within 60 days after the end of the tax year. A distribution from an IRA is taxable in the year of distribution unless it is rolled over (or converted to a Roth IRA) within 60 days. The distribution from the IRA would have to be done by December 31 of the tax year. Then, if the distribution is completed on December 31, the transfer to the Roth could be done within 60 days after the end of the year. If the transfer to the Roth fails for any reason, the distribution is taxable in the year it was distributed.

However, you can complete a recharacterization (reversal) of a Traditional IRA to Roth IRA conversion as long as the transfer is made by the due date of your return, including extensions.

 
Per IRS Publication 590-A Contributions to Individual Retirement Arrangements (IRAs), starting on page 23:

Time Limit for Making a Rollover Contribution

You generally must make the rollover contribution by the 60th day after the day you receive the distribution from your traditional IRA or your employer’s plan. 

The IRS may waive the 60-day requirement where the failure to do so would be against equity or good conscience, such as in the event of a casualty, disaster, or other event beyond your reasonable control.

Rollovers completed after the 60-day period. In the absence of a waiver, amounts not rolled over within the 60-day period do not qualify for tax-free rollover treatment. You must treat them as a taxable distribution from either your IRA or your employer’s plan. These amounts are taxable in the year distributed, even if the 60-day period expires in the next year. You may also have to pay a 10% additional tax on early distributions as discussed later in Pub. 590 under Early Distributions.

Converting From Any Traditional IRA Into a Roth IRA

Allowable conversions. You can withdraw all or part of the assets from a traditional IRA and reinvest them (within 60 days) in a Roth IRA. The amount that you withdraw and timely contribute (convert) to the Roth IRA is called a conversion contribution. If properly (and timely) rolled over, the 10% additional tax on early distributions will not apply.

Recharacterizations

You may be able to treat a contribution made to one type of IRA as having been made to a different type of IRA. This is called recharacterizing the contribution.

To recharacterize a contribution, you generally must have the contribution transferred from the first IRA (the one to which it was made) to the second IRA in a trustee-to-trustee transfer. If the transfer is made by the due date (including extensions) for your tax return for the year during which the contribution was made, you can elect to treat the contribution as having been originally made to the second IRA instead of to the first IRA. If you recharacterize your contribution, you must do all three of the following.

• Include in the transfer any net income allocable to the contribution. If there was a loss, the net income you must transfer may be a negative amount.
• Report the recharacterization on your tax return for the year during which the contribution was made.
• Treat the contribution as having been made to the second IRA on the date that it was actually made to the first IRA.

No deduction allowed. You cannot deduct the contribution to the first IRA. Any net income you transfer with the recharacterized contribution is treated as earned in the second IRA. The contribution will not be treated as having been made to the second IRA to the extent any deduction was allowed for the contribution to the first IRA.

Conversion by rollover from traditional to Roth IRA. For recharacterization purposes, if you receive a distribution from a traditional IRA in one tax year and roll it over into a Roth IRA in the next year, but still within 60 days of the distribution from the traditional IRA, treat it as a contribution to the Roth IRA in the year of the distribution from the traditional IRA.