Ayep. Modulo the fact that I've tended to focus on civil liberties as The Big Issue (with fiscal responsibility as a secondary), this is pretty much the approach I've been advocating for a good decade or so now.
I believe, though, that you have to get money involved. The rude fact is that money is what Washington listens to. If you can get a fund that's large enough to swing some key elections, *then* you really start getting Congress listening to you. Doesn't have to buy the elections outright -- just make enough difference to change the result.
Do that smart enough, and you may be able to forge an informal caucus on Capitol Hill. Get the congressmen you helped elect working together, and build up the notion of a joint identity -- "I'm a Democrat *and* a member of the Responsibility Brigade".
Indeed, I would probably recommend not calling the thing a "party" for exactly this reason. You can't afford to run your own candidates; instead, you're trying to swing the existing ones. The word "party" is a red flag, and invokes a lot of memes that aren't quite right.
Frankly, you need to recognize that it's very akin to what the religious groups do now on the extreme right, and that they've been fairly successful at it. Think about how to steal their better ideas and recast them in a secular mold.
And do keep in mind: the group you're talking about *does* more or less exist. It's the Concord Coalition
, founded a fairly long time ago, when the budget really started to spiral out of control. I was a charter member, but wound up lapsing because I've been unimpressed at their inability to organize and get out the vote. Take that group, give it more attitude and nerve, and you might have something...