There are good and bad ways to do this. Pethokoukis cynically, though probably rightly, imagines that the insurance premiums banks, or ultimately borrowers, pay for the guarantee will be treated like tax revenue. That, of course, would pervert the budgetary legitimacy of such a guarantee program. If mortgage insurance proceeds are treated like general revenue, then the government will just spend this money on things like entitlements or military, instead of throwing it in a vault to cover mortgages that go bad.
If the government does go with an explicit guarantee approach, then this should be done in a similar way to how the Federal Deposit Insurance Corporation guarantees bank deposits. Although the FDIC doesn't have a perfect track record, it has done relatively well over the years -- and responds appropriately by raising fees when it realizes it isn't charging enough for depository insurance. Here's how the mortgage guarantee program should work:
First, the government needs to have some criteria in place to ensure that underwriting standards don't get too wacky. Otherwise, it will run into the same problems that Fannie and Freddie did when they began loosening their credit standards.
Second, it should insure all mortgages up to some amount of their balance, say to half the median home price in the U.S., where the government takes the first loss. That would make losses to the private sector very unusual, except with very large mortgages. And such wealthy individuals would just be charged a premium by banks, which is politically palatable. Of course, the flip side of this approach is that it would make losses to the government far more likely, so it must charge sufficient insurance premiums to cover those losses.
Third, the agency in charge needs to make sure those premiums don't comingle with the government's general funds. If these funds are kept separate, then there's a chance taxpayers won't have to bail out homeowners going forward. This hope might be a little too optimistic, however, as it's rather likely that the government won't charge high enough premiums.
Fourth, to make sure funds aren't comingled, the government simply can't allow the Treasury to run this guarantee program. It can't be trusted. See Social Security. It needs an FDIC-like entity which the Treasury doesn't have discretion over. You could even argue that this new agency could be housed in the Federal Reserve so ensure political independence is achieved.
Finally, whatever agency is in charge of setting and collecting the insurance premiums must not sway with the economic cycles or political winds. No matter how safe mortgages appear over any given time period, the fees shouldn't be lowered significantly without very tangible evidence that a lower premium would still allow the fund to withstand even the deepest of economic shocks.
There are a lot of ways these guarantees could work. But these are some characteristics that any new federal program must include to have any chance of success. Otherwise, whether in several years or in several decades, when another housing collapse hits, taxpayers will be left holding the bill. That's precisely what a new system should seek to avoid.