Brown's head, and probably that of Alistair Darling, would almost certainly be the price of any such coalition.
This is problematic for a couple of reasons; firstly, Brown can't resign because (for various reasons of tradition) that would be extremely discourteous to the Queen (yeah, go figure; it makes little sense to me). If he's ousted, the alternatives are Harriet Harman, David Miliband, Ed Balls and Alan Johnson. You know both ends of the stick are shitty when I tell you that each of these people is less popular than Gordon Brown. In particular, Ed Balls is a well-loathed figure in British politics, but the ruthlessness and scheming for which he is loathed makes him a very serious contender for the job.
So we arrive at a coalition with another PM who didn't lead his party to an election victory, with a wafer-thin majority (Lib/Lab is 315, Con have 306 seats; the DUP will reliably side with the Conservatives (8 seats) and the other 20-odd independents and minor parties will go where the hell they like). The Conservatives will muller all but the least contentious legislation, and I don't reckon we'd get as far as September before the PM would have to go to the country or face a VONC.
Edit: Tidied up the numbers