THERE seems no end to the debate over whether President Reagan won or did not win a ''mandate.'' Few analysts see any major ''realignment'' as having occurred in the 1984 presidential contest - or the 1980 election, for that matter.
There is, however, one aspect involving ''mandates'' and ''realignments'' about which there is increasing agreement:
The relationship of political power between federal and state governments has undergone a major transformation during the past 10 or 15 years, accelerated by the transfer from Washington to state offices of responsibility over a number of social programs. That shift took place during the first Reagan term. The states now have a much larger role vis-a-vis Washington. And because of modernization programs involving better use of computers and streamlined legislative processes , many states must be considered role models of government at its best.
We mention all this because the states will now face a number of new challenges early next year:
* Political jockeying: Some hard bargaining at the committee level will be waged in most states, in part reflecting local election gains by Republicans. Republicans won some 300 additional seats. They will control 32 legislative chambers in January, compared with 66 for the Democrats. Ten years ago Republicans controlled 17 chambers, Democrats 81 chambers.
GOP gains were especially impressive in a number of Southern and Midwestern states. The GOP inroads are important for the party, as states look toward the redistricting that will follow the 1990 census.
* Slowing economy: The current cooling of the economy means continued - or higher - unemployment in some parts of the United States. The impact for states is twofold. There could be lower tax receipts as workers earn less or go on unemployment. Then, too, a slowing economy means the possibility of higher welfare and other support payments by states. Legislatures, which are in most cases required to balance their books, will have to once again examine the extent to which state services can be economically provided. Michigan, for example, has done well at the fiscal level of late. Any downturn in auto sales could increase layoffs and boost welfare outlays. And three states - West Virginia, Alabama, and Mississippi - still have double-digit unemployment.
Tax-limitation proposals were the big losers at the referendum level in the recent election. Voters now seem less hesitant about paying taxes for state services. That assumption, however, could be sharply tested if the economy continues to slow, or moves toward a recession.
* Issues: A number of somewhat contentious proposals will be coming up for consideration this next year, involving such matters as education (in particular , teachers' pay, merit pay, how much to spend on programs for the disadvantaged); how to comply with the federal-government-approved 21-year-old minimum-age drinking bill; how to promote economic development; how to provide for stepped-up environmental protection, now that the federal government is pulling back from environmental considerations.
In the weeks and months ahead, states must press hard to improve on the impressive economic and legislative gains they have made.