According the latest Washington Post - ABC News poll 52% of the public trusts the Democrats more than the Republicans to handle the federal budget deficit, while only 29% trusts the Republicans. In a television ad that Mitt Romney is running he refers to the Republicans in Congress as "acting like Democrats" when they irresponsibly run up the deficit. Of course, this ad is aimed at the Republicans who will vote in the primaries and caucuses. I assume this ad works for him since the target of the ad is people who are in the 29% who think that acting like a Democrat is a bad thing.
I assume that if Mitt Romney wins the Republican nomination then during the general election campaign he will have to start promising that in fiscal matters he will emulate the Democrats since at that point he will be addressing the 52% who think that in fiscal matters acting like a Republican is a bad thing.