The free service right now (having a 'mini newspaper' emailed to you every morning) is nice, but to be honest, I would value this at about $1/month, but I might pay up to $1.50/month to support journalism. I suspect that they will want to charge more than this.
And at $1.50 it's not going to be a particularly good cup of coffee.
But I'm in the same boat. I already shell out ~$100 a year for the Economist, and various other subscriptions. If I have to start paying for all the news SOURCES I read I'm going to be out a great deal more. Note I said SOURCES. I'm willing to pay for news, but not a monthly subscription to a news site I only read occasionally.
This almost sounds like you'd be willing to pay dues to the AP or Reuters. I don't think that's such a bad idea. I know it would never fly in America but a funding system similar to the BBC, where households have to purchase licenses for things, might work well.
Maybe there's a business model to be had for a decent aggregator? I know I'd pay (how much is the sticking point) for a nice mashup of NYT, WSJ, and Economist content. That might be my dream news publication, actually.