Republicans in Virginia's House of Delegates, their political hopes already bolstered by a popular GOP president, are now cautiously predicting that this week's redistricting decision by a federal panel could set the stage for strong GOP House gains in 1982.

The three-judge panel ruled that the redistricting plan drawn by the House of Delegates is unconstitutional and ordered that House members elected under it this fall stand for reelection next fall under a revised plan.

That means, Republicans say, that Virginia's statehouse candidates will be able to grab onto the coattails of the state's congressional delegation -- which is dominated 9-to-1 by the GOP.

"This is bound to help the Republicans," said Del. Vincent F. Callahan (R-Fairfax). "This is one of the most significant things that will come out of the court decision, and I think it will bring some significant gains."

Republicans also say they are hopeful that the panel's stated preference for single-member districts could back the Democratic-dominated General Assembly into approving a plan that boosts GOP chances even more. They believe that a single-member district plan would aid Republicans by creating more and smaller districts in which pockets of Republicans would not see their voting strength watered down by larger surrounding populations of Democrats.

"I really don't see how the General Assembly can do anything but follow one of two options: either they'll approve a single-member district plan or a plan with a large proportion of single-member districts," said House minority leader Jerry H. Geisler (R-Carroll).

Analysts say the passage of a single-member district plan could help the GOP gain up to a dozen seats next year in the Virginia House of Delegates, the state's last major bastion of Democratic political power. If so, the state could see an end within the next few years to more than a century of Democratic Party dominance of the 100-member House of Delegates.

"With the election scheduled for 1982, and the Republicans running their big guns all over the state, it could become the first real step toward a GOP legislature," acknowledges Democratic political strategist Paul Goldman.

Still, the Republican road to electoral success is far from assured. Many assembly members, including Democratic caucus leader C. Hardaway Marks of Hopewell, are calling for the state to appeal the three-judge panel's decision to the Supreme Court. Court challenges are also being considered by the American Civil Liberties Union and Common Cause.

A Supreme Court reversal of the panel's decision could create a whole new set of requirements for the state redistricting plan, including a winter or spring election. That would pit the Republican brand of well-funded, high-technology politics against the Democratic organization, a loose coalition of local courthouse officials, without the aid of any federal or statewide races to turn out the vote.

Republicans also caution that the congressional coattail effect, which they are counting on as a positive factor, could possibly work against the state GOP in a fall 1982 election. "It depends on the Reagan administration," said Del. Clinton Miller (R-Shenandoah). "If the economy is still in a slump, it could be counterproductive."