Question: I am currently employed by a major consulting firm, where I work on a contract for a federal agency. I recently recieved a final job offer and EOD from this same federal agency, which I've accepted. I told my manager at the consulting firm about my plans and gave her several weeks notice. However, this manager told me she would talk with her contact at the federal agency about delaying my EOD or having me spend my first few months of federal employment working on her contract. Is it possible that the federal agency would modify my start date at her behest?

Answer: 
It's unlikely that she'll be able to delay your end date at her company, but it's possible that you could end up working on her project at your new job. But it doesn't come down to what you want; it's up to the federal agency to decide, and they may or may not want to give your previous employer what she'd like.
While I have never gone from non-government to government employee, I have seen it done a number of times.

If you are going to end up working for the same agency in the same region I have seen the government managers negotiate a deal where for X months you will be available to provide a limited amount of assistance. But during that time you remain a government employee.

I have also known when the new manager doesn't cooperate and the employee is blocked from providing help, though I have seen a few cases where they snuck in a few hours in a crisis. The risk for the employee is if they get caught, or if the old project starts demanding too many hours.

I have never known a manager to be able to delay the start date unless the the employee would be moving to the same project and there were budget or logistical reasons.

why does your manager want to delay your start date besides the normal concerns of a departing employee? I have seen these a few times:

* Money. They can't bill for your hours anymore and they are concerned that it will take time to fill the slot.
* Contract. They are obligated by the current contract to fill that position in X days or they will face punitive damages that goes beyond the lower amount they can bill.
* Competition. They fear that the government will decide that a competitor can fill the position, and award that part to a competitor.
* Future. They fear that the government will be slowly bringing jobs in-house, which will mean eventually the contract will be cancelled.

These are real concerns. But they are unlikey to persuade a government agency to delay your start date.