Are Republicans falling into a trap by tying raising the debt ceiling to budget cuts?

I just had an odd thought.  Republicans have drawn a line in the sand:  no new taxes, no restoration of the old tax levels, all deficit reduction must be accomplished by budget cuts.  This is a fairly extreme position.  While most Americans aren’t eager to have tax increases, I think most reasonably feel that the deficit is so large that the only practical way to even begin to rein it in is by both raising taxes and cutting spending.  Anyway, the Republican have taken this stand and tied it directly to raising the debt ceiling.  [As an aside, I think they will either have to back off of this position, allowing tax increases, or accept deficit reductions far too small to even begin to solve the problem.  Perhaps they are just taking a hard negotiating position to see who blinks first, but I think they are setting themselves up to fail.  We shall see.]

But, isn’t this all backwards?  The implication if the Republican position is, gee, we’d like to do all of the things the government is doing, but we can’t afford it.  By making this all about the budget deficit and the debt ceiling, rather than saying there are many things (mostly redistributions of income) that the government shouldn’t be doing at all, we’re saying we’re too broke to do them.

I’ve fallen into this trap myself.  I’ve said on this blog that I think our government should do what real people do — figure out how much money we have, then budget what we are going to do with that money.  When the government runs out of money, it should quit spending.  Perhaps, however, the government should first figure out what it wants to do, and what it shouldn’t be doing, then budget to make sure it has the money to do what it wants to do.  What do you think?