Washington — Jim Watt must be finding this an oddly satisfying week. On Monday, environmental leaders dumped petitions on the Capitol steps from more than 1 million Americans calling for his ouster as secretary of the interior. On Wednesday, environmentalists testifying on Capitol Hill were praising Mr. Watt - who sat smiling just a few feet away - for his position on what could be one of this session's most important measures to protect the environment.
This happier latter coincidence for the embattled interior secretary focuses on safeguards for the thousands of miles of barrier islands along the Atlantic and Gulf Coasts. For years, conservationists have argued that government policies have subsidized and therefore encouraged development that is harmful to these fragile areas. The Reagan administration agrees, and wants to apply its ''free-market'' economic concept in a way that could prevent further harm to vast coastal stretches from New England to Texas.
On Capitol Hill, there is growing bipartisan support for legislation that would end federal funding for construction programs on undeveloped barrier beaches and islands. This includes money for bridge, road, and sewer construction, loans for economic development and home building, and federal flood insurance.
The Interior Department estimates that nearly half a billion dollars was spent on barrier island development between 1976 and 1978, and that Uncle Sam could spend as much as $11 billion on such programs over the next 20 years if nothing changes.
Aside from the monetary cost (much of which benefits the owners of expensive vacation homes), environmental concerns are mounting as well.
''The importance of barrier islands and beaches as storm buffers for the mainland, and the economic value of their fish and recreational resources is unquestioned,'' says Jay Hair, executive vice-president of the National Wildlife Federation. ''The paradox of barrier islands is that they must be in constant flux to remain in equilibrium with the immense power of the ocean.''
Development in these areas, it is pointed out, not only amounts to a ''building on sand'' that is frequently dangerous and costly to man, but accelerates the erosion that can lead to an island's destruction.
In his Senate testimony this week, Interior Secretary Watt agreed with those calling for greater environmental protection of the barrier islands and beaches. But he also emphasized the growing costs of past government intervention.
''Taxpayers subsidize initial development, a hurricane sweeps the area, the taxpayers via government assistance encourage rebuilding, and the cycle begins again,'' he said.
As an example, others point to the experience in 1979 when hurricane Frederick swept across Dauphin Island in Alabama causing property losses totaling more than $2 billion. The federal government will help pay for the rebuilding, including 90 percent of the $34 million cost of replacing the bridge to the mainland. This alone will amount to $50,000 for every island resident.
Others argue that without federally subsidized flood insurance, such losses would have to be made up by the government anyway in the form of federal disaster assistance and lost tax revenues.
''I would suggest that restricting the availability of flood insurance will inevitably increase the overall cost to the taxpayer,'' says Jim Scott, a South Carolina developer speaking for the National Association of Homebuilders.
Others call federal attempts to control development on barrier islands a form of ''redlining'' that infringes on local zoning and land-use planning perogatives.
But the movement in Washington is for just such controls. This year's budget reconciliation act already cuts off the possibility of federal flood insurance on undeveloped barrier islands and beaches after September 1983.
Legislation prohibiting federal spending on loans and grants for future development in such areas is given a very good chance for passage, probably early next year. Especially since environmentalists and Interior Secretary Watt have found an issue on which they can agree.