What will the Democrats do with their majorities in Congress? The 2006 campaign was pretty much an idea-free zone and provides only a few clues. In their hearts, most elected Democrats would like to move us some distance closer to a European-style welfare state — slouching toward Scandinavia, some conservatives might call it. But they are likely to find it difficult to do so, and not just because of President Bush’s hitherto almost unused veto power.

Take the proposal they usually put first on the list: raising the minimum wage. Only about 2% of earners now make the minimum, and some jobs will disappear when it’s raised. Moreover, most minimum-wage earners are not heads of households. Any progressive economic redistribution will be minimal.

Even liberal economists agree that you’d get much more redistribution by expanding the earned income tax credit. But that could increase the marginal tax rate on low earners at the point where the EITC tapers off, unless tax rates are cut.

Democrats might be inclined to do that, but it would be at a heavy cost. That’s because the Democrats have sworn to reintroduce “pay-go” rules on tax cuts. That’s a backward-looking move: It would have made it harder for recent Republican Congresses to cut taxes. But it will force Democrats, if they want to cut low earners’ tax rates or extend the middle class portions of the Bush tax cuts beyond 2010, to find compensating spending cuts or tax increases.

It will also make it harder for Democrats to do something they must do for political reasons — adjust the Alternative Minimum Tax. The AMT was passed in 1969 to ensure that no one could totally avoid taxes. It sets up a separate income tax system, without many normally applicable deductions. Because it has not been indexed for inflation, it’s slated to apply to rapidly increasing numbers of taxpayers with incomes around $100,000 and lots of deductions in high-income Democratic states like New York, New Jersey, Connecticut, Illinois, and California.

Congress has been adjusting the AMT year by year. The high revenue projected in out-years makes it impossible to abolish under the pay-go rule, and even an annual fix is very expensive. But an important Democratic constituency — public employee unions — has a vested interest in adjusting the AMT. AMT taxpayers can’t deduct the high state and local income taxes in these states, and may be motivated to vote to cut the state and local taxes that are the public employee union’s lifeblood.

Democrats may be able to pass bills raising taxes on high earners and raising the 15% rate on capital gains and dividends. But such bills are almost certain to be vetoed, and the response to the 1993 Clinton tax increases suggests that “soak the rich” is not a sure winner in elections.

Increased deductions or tax credits for college tuition is on the Democrats’ to-do list and would certainly be popular with beleaguered parents. But colleges and universities have been sopping up previous tax breaks by raising tuitions at above-inflation rates, and presumably would do so again.

Thoughtful Democrats like Clinton aide Gene Sperling and Yale professor Jacob Hacker have argued that Americans, even amid prosperity, are increasingly insecure in our globalized economy and wary of downside risks if they have to change jobs or learn new skills. They look back with nostalgia sometimes toward the unionized lifetime jobs many held 50 years ago in mid-century America, and argue that government needs to provide more protection against risk.

The problem is how to do it. Congress cannot recreate mid-century America by snapping its fingers, and the seemingly risk-free health benefits and pensions that unionized companies promised are now in peril because the business model of firms like the Big Three auto companies, the old-line steel companies, and the legacy airlines has become unsustainable.

One interesting proposal by Mr. Sperling is for a “universal 401(k),” which would give all workers tax-sheltered savings accounts, funded by employers and employees. One option is to give low earners tax credits, perhaps even refundable tax credits, for their contributions to the accounts. Over time, this would increase low earners’ wealth accumulation — progressive redistribution. But it would also tend to transfer funds from the federal treasury to individuals, from the public sector to the private sector — not the direction Democrats usually want to go.

It’s a proposal that looks a lot like the Social Security individual investment accounts President Bush called for, and Democrats scorned. It would be ironic if this turns out to be the major progressive achievement of this Democratic Congress.