Washington — The Democrats are awakening, their political antennas telling them that President Reagan is perhaps becoming vulnerable. They look at the plunging stock market and see in it both a vote of nonconfidence in Mr. Reagan's economic policies and an indication that his honeymoon may be ending.
The signs of a new Democratic stirring:
* Democratic leaders at federal, state, and local levels have finally agreed to join together in a group called the Democratic Strategy Council.
Senate and house leaders will soon be meeting with governors, mayors, and party chieftains to map plans for raising the level of opposition to the Reagan administration.
* Democrats are moving to improve their presidential nomination process to make sure that the Democratic standard-bearer in 1984 is the best and most potent candidate avalable.
Party machinery is at work to make a place for top officeholders and party chieftains at the next national convention. The party wants the wise counsel of these veterans at the 1984 gathering. At the same time, the Democrats intend to retain the reform formula that has guaranteed strong participation by minority delegates at the convention.
* A new organization, the Center for Democratic Policy, is preparing position papers which it hopes will provide Democratic officeholders and candidates with new, persuasive themes.
Ted VanDyk, president of the center, says that "Labor Day will mark the end of the Reagan political honeymoon,." He says that from that point on the President will be with difficult decisions, the kind that are bound to erode his public standing.
Mr. VanDyk, talking to reporters over breakfast Aug. 25, noted that Reagan's most difficult job will be to find more budjet cuts if he is to persist with his goal of beefing up the military.