DES MOINES — The ailing economy and the Tea Party’s demand for smaller government have dominated Republican politics for two years, but a resurgent social conservative movement is shaping the first stage of the presidential nominating contest, complicating the strategy for candidates who prefer to focus on fiscal issues over faith.

Here in Iowa, whose caucuses next winter will open the campaign, social and religious conservatives are pressing the likely candidates on issues like same-sex marriage and abortion rather than on jobs, the budget deficit and other economic concerns that leaders of both parties expect to dominate the general election.

The development provides opportunities for candidates like Representative Michele Bachmann of Minnesota and former Senator Rick Santorum of Pennsylvania, who have a following among social conservatives. But it could make Iowa even more difficult territory for, among others, Mitt Romney, the former Massachusetts governor, who has yet to visit the state this year.

More broadly, some Republicans say, it could muddle the party’s message as it seeks to defeat President Obama.