In anticipation of the looming first-time homebuyer tax credit expiration, home builders are hedging their bets on speculative construction in the hopes that the extended April 1 deadline will incite a frenzy of last-minute purchases. On the one hand, this strategy would appear to make sense: the last time the tax credit was supposed to expire, on Nov. 30, 2009, there weren’t enough new homes to meet the demand from new buyers, and builders lost out on a lot of potential sales. But on the other hand, experts say builders are taking a huge risk because at this point, most first-time homebuyers who want to take advantage of the federal program have already done so. If the new, speculative construction homes don’t sell to a wave of first-timers, they might end up back on the market at steep discounts, which could ultimately slow the housing recovery. For builders who do decide to up their inventory, they’ll have to do it soon. It takes between four and six months to build a house, and at the end of 2009, the number of homes for sale was at 234,000, the lowest level since April 1971, according to the National Association of Home Builders.