Liberal Democrats and civil rights groups are pushing to complete House action on an extension of the Voting Rights Act this summer, but the Reagan administration has sent signals that it isn't going along for the ride.

Rep. Don Edwards (D-Calif.), chairman of the House Judiciary subcommittee on civil and constitutional rights, has held extensive hearings on the bill and said he plans to start marking it up after the July 4 recess. "We hope to have it out of the full committee before the August recess."

The administration has yet to take a position on the measure, however, and the Justice Department took the unusual step recently of declining Edwards' invitations to testify on the bill.

The public explanation is that the department is waiting until its new civil rights division chief, William Bradford Reynolds, is confirmed by the Senate. Privately, though, several administration officials and Republican congressional aides said political considerations also are a significant reason for the delay.

"It was brilliant politics for the Democrats to seize on the issue as they have, but it's in the president's interest now to minimize the interest," one Hill aide said. "There's a lot of politics as well as a lot of legitimacy in this one. They are making any Republican who raises a question look like a racist," another said.

"There's just no reason for us to march to Don Edwards' agenda," one administration official said. "Why should we make somebody mad in June of '81, when we've got another year to act?"

Thus it wasn't surprising that President Reagan fuzzed the issue in yesterday's speech to the NAACP, nor that he sent a letter to Attorney General William French Smith some days ago, telling him to take until Oct. 1 to make a thorough review of the legislation.

There had been some concern at the Justice Department that the White House might want to decide on a position in time for the president's speech. Smith has been discussing a range of proposed changes with civil rights and other groups in recent weeks and aides said they welcomed the breathing space the president's letter gave them.

The key and most controversial provision of the law, section 5, requires states which have had a history of racial discrimination to get Justice Department "pre-clearance" for any changes in their local voting laws.

Many witnesses at the Edwards' hearings testified that the act is the most significant civil rights bill ever passed because it has boosted black voting registration in the South. The special provisions still are needed, they said.

Opponents say southern states are unfairly carrying a burden long after they stopped discriminating against blacks, and the "pre-clearance" procedures should be dropped, as scheduled, in August, 1982.

Rep. Henry J. Hyde (R-Ill.), the ranking minority member of Edwards' subcommittee, is considered a pivotal figure in the evolving debate, and proponents of a strong bill have been encouraged by his actions.

Hyde first introduced a bill to alter the pre-clearance procdures, noting the Justice Department had objected only to about 800 of 35,000 proposed voting law changes since the act was passed in 1965. After listening to the testimony at the hearings, however, he changed his mind.

Last Wednesday, he introduced a new bill that would extend the administrative pre-clearance indefinitely, while offering a "bail out" incentive to jurisdictions that can show they have not discriminated against minorities in the past 10 years.

Hyde said he concluded from the hearings that "there are some jurisdictions which deserve to remain covered, both because there are persistent vestiges of discrimination present in their electoral system and because no constructive steps have been taken to alter that fact."

In a "Dear Colleague" letter last month, Hyde recognized the political sensitivity of the issue.

While the original House bill would extend the pre-clearance provisions for 10 years, "I believe it is fair to say that there are some individuals in the other body who would like to see the pre-clearance provisions expire altogether in 1982. This conflict of views puts President Reagan and the Republicans in the Congress in a rather sticky political situation."

Sen. Strom Thurmond (R.-S.C.), chairman of the Senate Judiciary Committee, already has voiced concerns about the act and his committee clearly is in no hurry to move on the extension legislation.

Edwards said in an inteview that he was pushing for early House action to give the Senate time to act.

He recalled losing new Fair Housing Act remedies last session when House-passed changes were killed by last-minute Senate inaction. "It is a very simple bill. The evidence to support it is overwhelming. I'm sure the party of Abraham Lincoln will support it."

Another Democratic strategist acknowledged the early House action was designed to give the civil rights community a year to lobby the Senate . . . . If there were any geniuses in the Republican Party, this is one bill they would go with and try to take credit for. Thank goodness they're not. They're going to blow it."

Kenneth Starr, the attorney general's counselor, said that in his recent discussions with interest groups, Smith has mentioned several possible administration positions on the act. They range from letting section 5 expire to continuing it for 10 years. Other possibilities include:

Extending the pre-clearance provisions to the entire country so every jurisdiction would have to get Justice Department approval before changing voting laws.

Retaining the pre-clearance provisions, but restricting them to the changes mostly likely to cause discrimination, such as annexations, or changes from single-member to at-large elections.

A "bail out" provision similar to the one in Hyde's latest bill.

Retaining pre-clearance, but changin g the formula of what jurisdictions are cvered. For example, a wide disparity of black-white registration might be offered as a trigger to replace the current definition of states or jurisdictions that had less than a 50 percent voter turnout in recent presidential races.

Replace the pre-clearance provisions with a requirement that jurisdictions give "mandatory notice" of voting changes. This would shift the burden of proof of discrimination from the state or locality to the attorney general.

Eliminate pre-clearance, but amend the nationwide provisions of section 2 of the act so that jurisdictions could be found guilty if voting changes had a discriminatory "effect" as well as "intent."