There was a time in the not-to-distant past when the Democratic Party was considered the party of deficit spending. We were, after all, the party most commited to Keynsian economics--the idea that recessions should be handled by having the government pump money into the economy by spending more than it recovered in taxes, then keeping the economy in check in good times by raising taxes.
Since Mr. Clinton's presidency, most liberals have more or less abandoned Keynsian economic theories. Under Mr. Clinton, the budget came into balance as the economy boomed; by 2000 the government was running a considerable surplus and beginning to pay down long-term debt. Keynsian economics had two practical problems. First, the US government moves very slowly by design, so by the time the deficit spending designed to fight a recession began, the recession was often over. Worse, it's much easier for the US government to begin deficit spending than to end it--tax cuts and new services are almost universally popular, while service cuts and tax hikes are almost universally unpopular.
What's wrong with the government running in deficit, as it has done throughout Mr. Bush's presidency? If deficits are small and for specific, nonrecurring purposes (to fight the Iraq War, for example), deficit spending makes some sense; it allows the government to pay for crisis over a long period of time. Unfortunately, the bulk of the recent deficits have been caused by the tax cuts Mr. Bush has implemented. This means that the government is running a structural deficit--that is, it would be in deficit even if we weren't fighting a war. Structural deficits, if they aren't addressed, eventually make bond investors wary; to protect their investment they may begin to demand higher interest rates. At that point we have a serious problem--either consumer interest rates go up (making life very difficult for homeowners with adjustable-rate mortgages and for anyone with a lot of credit-card debt) and the deficit gets much worse (because the cost of "servicing the debt"--paying interest on the existing debt--increases), or the government simply prints a lot more money, causing sharp inflation.
Note that this is one issue on which libertarians and liberals actually have more in common with one another than with conservatives. Libertarians generally want a very small government indeed, paid for by small (but adequate for the task) tax rates. Liberals generally want a larger government, financed by taxes more like those we had in the 1990s. Conservatives want the larger government as well (judging by their actions since they won effective control over the government in 2002), but want lower taxes; they theorize that these lower taxes will cause an economic boom that will actually increase tax receipts. Sometimes this works (it did under Mr. Reagan, although the government grew faster at the time than did tax receipts), but so far it hasn't under Mr. Bush.
It is, broadly speaking, the liberal position that increasing interest rates are a much greater threat to the economy than taxes at 1990s levels were. Moreover, it the tax cuts were aimed at boosting the economy in the short term, they weren't structured well. The problem here is philosophical--if you want to pump up a faltering economy, should you aim tax relief primarily at families that earn $30,000-$100,000 per year, in hopes of boosting spending, or at families earning above $200,000 in hopes of boosting investment. Mr. Bush's administration has opted for the latter course, with predictable results; the stock market has been booming, but working families are struggling. Liberals would have opted for the former course.