A group of Democratic senators plans this week to take the unusual step of demanding on the Senate floor that the Pentagon's $180.3 billion procurement bill be sent back to committee because it is too high.

Sen. Carl Levin (D-Mich.) was putting the finishing touches last night on a motion to recommit the defense bill to the Senate Armed Services Committee that approved it earlier this year with only one dissent--his. The Michigan senator will argue that the economy has sunk so low that the nation cannot afford to finance a record defense bill in fiscal 1983.

Allied with Levin in this effort as of last night were such Senate Democratic leaders as Robert C. Byrd (W. Va.), the minority leader, and Ernest F. Hollings (S.C.), ranking Democrat on the Budget Committee.

They were seeking to round up some Republicans to make the recommital effort bipartisan, but prospects for this looked dim. A number of Republican senators approached agreed that the committee bill is moot in the sense that even President Reagan has signaled that he will settle for less than the $180.3 billion the committee approved for ships, missiles, aircraft and other weaponry in the new fiscal year.

However, the Republicans balked at the prospect of looking soft on defense or being critical of the administration.

Although the vote counters were resigned to seeing the recommital motion voted down today, they said the attempt would dramatize signficant support for these three propositions:

That the Armed Services Committee should not push a bill through the Senate before the Budget Committee has set a ceiling for national defense.

That the Pentagon no longer can be kept off limits when it comes to reducing federal spending to lower the deficit.

That the Armed Services Committee should take the final figure agreed upon for procurement in fiscal 1983 and figure out how to reach it after careful deliberation.

The statements being drafted last night by backers of the recommittal motion stressed that they were neither against a strong national defense nor trying to make political points at the expense of Republicans.

Despite such disclaimers, the mini-rebellion over approving the defense bill before the Budget Committee has acted amounts to a slap at Chairman John G. Tower (R-Tex.) of the Senate Armed Services Committee. He rushed the bill to the floor, without ever hearing from Defense Secretary Caspar W. Weinberger during an open hearing by the full committee, some senators have protested.

Tower's strategy was to exert leverage on the Senate Budget Committee to approve a high figure for national defense. But critics said that his attempt to do this at the time President Reagan is leaning toward a lower figure makes the committee bill irrelevant.

Sen. John C. Stennis (Miss.), ranking Democrat on the Armed Services Committee, said as the debate on the procurement bill opened yesterday that his preference when he chaired the committee was to let the Budget Committee set the figure first to keep the authorization process from becoming "irrelevant." However, Stennis did not object to taking up the bill yesterday and thus supported Tower's fast track approach.

Tower, in his opening statement, said that "we simply have no choice" but to vote almost the full amount that Reagan has requested for national defense. "The threat facing us demands that we endure sacrifices, sacrifices that we must endure for the common defense."

To help senators assess the Soviet threat, the Senate will hear in closed session today from government intelligence executives about Russian military programs. The debate on the defense bill is scheduled to follow that briefing, with the recommital motion expected to be offered early in the proceedings.

The Senate committee's recommended total of $180.3 billion compares with $183.4 billion requested by the administration, a reduction of $3.1 billion.

In budget negotiations last week the White House put on the table a series of proposals for reducing defense spending between $23 billion and $33 billion over the next three fiscal years. The proposed reduction for fiscal 1983 of from $4 billion to $6 billion would be in spending, requiring a larger reduction than that in the amount appropriated since those funds are spent over several years.