CMO's famously now have bigger IT budgets than the CTO.
As someone who makes and sells marketing software, for me, this is great news. For the CMO's however, it may not be. They are now in charge of very significant technical projects - sometimes genuinely massive - yet they are likely 5 or so years light on technical training, and 20 years in the field, against their CTO peers. A huge shortfall.
This is by no means to say that the CMO is deficient in some way - set the CTO on your marketing for a good demo of that - but it is nonetheless true that marketers do not have deep training in some key technical areas.
Take, for example, 'the new website'. The highly skilled CMO at the top of their game has probably been involved in three or four at most. And the learning from each would be scant; the knowledge gained in 1999 would be irrelevant to the point of dangerous in a modern web project. Nonetheless, it is the marketers job to deliver the project.
So my one piece of advice is to treat it as a marketing exercise - because it must remain that - but make sure that it is delivered using technical project management best practice.
So do one of two things:
If you are building the website, in-house or externally, make sure that you use agile processes* in your project management and ensure that you have calls weekly, or even daily, with the team. Make baby steps every day with milestones every 2 or 3 weeks (the sprint cycle). Institute this rigor early so that when the deadline comes, though you won't have everything you want (I promise you that), you will have something!
But, better, put the time in early to find the solution that is already built so that the level of customisation is around brand, not functionality. Now it really is 'just' a marketing project - copy, brand and all the good stuff. Then you really should be able to deliver on-time and in-budget.
* If you buy any well reviewed scrum/ agile project management book and read the introduction and the first couple of chapters you will have a good grasp.