It was only symbolic gamesmanship, but the Senate yesterday handed the Reagan administration one of its first clear defeats in a vote on the president's proposal to hold down milk price supports.

The White House and the Republican Senate leadership have until Thursday -- when the issue will come again -- to change enough minds to reverse yesterday's 53-to-45 outcome. If they fail, President Reagan will suffer an embarrassing loss to the milk lobby.

That hard-working group set up yesterday's vote with considerable skill by avoiding a confrontation on the specific issue of milk price supports. The big diary organizations have decided that Reagan cannot be stopped in his effort to skip a scheduled April 1 increase in the basic support level, which would cost the federal treasury $147 million this year, and would add up to 15 cents to the retail cost of a gallon of milk.

Having all but given up on winning the April 1 increase, the dairy industry concentrated on a much narrower issue, hoping to win a symbolic victory as a show of strength to be exploited in future confrontations with the new administration. The issue the lobby chose to fight was imports of casein, which is powdered pure milk protein used to make products ranging from paint to coffee whitener and imitation cheese.

For yesterday, at least, the milk lobby's interests coincided with those of Senate Democrats, who were looking for a chance to demonstrate both party discipline and the power to frustrate the new Republican majority.

The vehicle for the vote was an amendment proposed by Sen. John Melcher (D-Mont.) to the administration's bill on the April 1 increase, an amendment that would limit casein imports to half their average level over the last five years.

Melcher, Patrick J. Leahy (D-Vt.) and others who supported the amendment admitted that it might violate the General Agreement on Tariffs and Trade (GATT), but this did not prevent them or a long list of free trade, liberal Democrats from supporting the Melcher proposal. Melcher argued that imported casein displaces domestically produced powdered milk, reducing consumption when the government is forced by law to buy up big domestic surpluses.

Speaking for the administration, Sen. Jesse Helms (R-N.C.), chairman of the Ariculture Committee, pleaded that reducing casein imports would do little or nothing for dairy farmers while complicating trade relations with important allies.Majority Leader Howard H. Baker Jr. (R-Tenn.) moved to "table" -- to kill -- Melcher's amendment.

Eight Republicans from farm and dairy states joined 45 Democrats who refused to table the proposal. Normally, a failed vote to table would be followed by an up-or-down vote on the amendment. But Baker, saying "I accept there are minds to be changed," instead quickly brought the Senate's business to a close, postponing a final vote until Thursday.

Sources on both sides said last night the administration has a good chance of prevailing Thursday. But the dairy lobby and the Democrats enjoyed the opportunity to send a message yesterday. "They're so arrogant," Leahy said last night. "Now maybe they'll listen."

In the House, key members of the Agriculture Committee want to see an outline of the administration's overall plans for the dairy program before agreeing to skip the April 1 adjustment.