House Republicans are stumbling over one another as they rush into the nunnery, hoping to distance themselves from the corrupt lobby culture they helped create. You can bet on this truth: The successor to Tom DeLay as majority leader will push all sorts of lobby reforms while DeLay and his running buddy Jack Abramoff are stuck in the courtroom.

But here's another truth to bank on: It's a mistake for House Republicans to get so deep into their nunnery that they miss the additional issues that could alienate them from everyday voters — and their Republican base. Cleaning up Washington is important, but other problems affect Americans more directly and could impact the 2006 and 2008 elections. Let me offer three examples:

The Greenspan challenge

House conservatives like GOP Rep. John Shadegg of Arizona are hep on ending earmarked spending requests. Fine. No more special funding items that lobbyists get legislators to slip into bills. Earmarks run up the deficit and encourage a bribery culture.

But what about gutting up to Alan Greenspan's challenge?

The retiring Fed chairman asked Congress last fall to return to its old practice of paying for spending hikes and tax cuts by reducing spending elsewhere. Congress employed pay-as-you-go rules in the 1990s to help balance the budget. With Katrina and Iraq pressuring the budget, Greenspan thinks the deficit's reached the place where Congress needs to reinstate these rules. (The deficit stands around $325 billion.)

You'd think House Republicans would take the fiscal conservative of all fiscal conservatives at his word. Shadegg and others, including Texas GOP Rep. Jeb Hensarling, pride themselves on being stewards of the nation's purse.

So far, they haven't. In fact, House Republicans will soon consider cutting taxes by up to $95 billion over five years — without offsetting them with enough spending cuts. The Congressional Budget Office projects that the tax cuts will swell the deficit.

Here's to hoping they wise up and meet Greenspan's challenge, which, by the way, the conservative budgetmeisters at the Committee for a Responsible Federal Budget and Concord Coalition support wholeheartedly. Reductions like lowering capital gains taxes can stimulate the economy, but they don't make sense if the expense worsens the deficit.

Alternative minimum tax

Talk about a threat to many Americans. Congress set up the alternative minimum tax in 1969 to make sure the super-wealthy pay some taxes, instead of escaping them through loopholes. Now, the so-called AMT is about to snare middle- and upper-middle-class taxpayers. When it does, Republicans running the House will hear bellowing across the land, including from the professionals they depend upon for votes and contributions.

To be fair, you can't really blame Congress for postponing this problem until now. A real fix, one that would change complicated formulas that are pushing the tax down to the middle class, could cost $375 billion over 10 years.

But if House Republicans want to govern, they've got to tackle the big ones. They don't get much bigger than this.

Immigration

The House passed legislation in December that would erect a wall between parts of the United States and Mexico and put more agents on the border. The Senate and President Bush want a broader plan. They advocate a guest worker program that would allow foreign workers, including illegal immigrants, to apply for three-year visas.

If the Senate passes such a plan in the next two months, will House Republicans go along with it? Or will they only scream about a fence and more agents?

Some House Republicans probably think they need to play to the talk-show crowd that's demanding a fence. But their new majority leader should encourage them to review a survey last fall by the conservative Manhattan Institute.

It reveals that likely Republican voters don't — repeat don't — want an immigration bill that only toughens up the borders. They also want a plan that allows illegal immigrants to earn citizenship while working here. Otherwise, we'll never get a handle on the immigration mess.

There are plenty of smart Republicans who know there's more to governing than taking on the lobby. But will they step up to the challenges? They'll have a lot riding on their answer in November.