A strong conservative effort to block the nomination of Frank Reiche to a Republican slot on the Federal Election Commission is expected to culminate today or tomorrow with a filibuster attempt by Sen. Gordon Humphrey (R-N.H).

Many conservatives, both inside and outside the Congress, regard Reiche as insufficiently partisan to represent the party on the highly partisan commission, even though his name was submitted to the president by House Minority Leader John Rhodes (Ariz.) and Senate Minority Leader Howard H. Baker Jr. (Tenn.).

Some Baker allies also see the movement against Reiche as an attempt to embarrass Baker, a potential Republican presidential candidate with slim ties to the party's right wing.

Reiche, a Princeton, N.J., lawyer, was chairman of the New Jersey Election Law Enforcement Commission for six years. In his New Jersey post, he was not permitted to engage in partisan political activity, though he served as a Republican county committeeman for eight years before his appointment.

Most FEC members have been defeated members of Congress or highly partisan political activists being rewarded for years of party service with the $50,000-a-year posts.

Humphrey has cited Reiche's unwillingness to come out against public financing of congressional elections as the primary reason for his opposition. Beyond that, said Humphrey aide Don Shasteen, Reiche is "out of step with Republican positions and would not strongly represent the Republican point of view."

The FEC consists of three Democrats and three Republicans. On highly partisan issues, its 3-to-3 votes prevent any action damaging to one party or the other. Reiche's opponents are afraid that his appointment might upset this balance.

Shasteen said that "Senator Humphrey has really writhed in pain" over the suggestion that the anti-Reiche movement is really an anti-Baker effort.

He acknowledged that at one point in an anti-Reiche strategy session, some had suggested using the issue to call for Baker's resignation as minority leader."But Senator Humphrey said he would not be a part" of this, Shasteen said, and the suggestion was not considered seriously.

Word of the episode leaked, however, weakening Humphrey's position and lessening support for it in the Senate. Originally, 23 Republican senators had placed "holds" on the Reiche nomination. The number is now thought to be 16 to 17, with Humphrey and Sen. Paul Laxalt (R-Nev.) Reiche's staunchest opponents.

"I think they're ignoring the fact that I have labored in the Republican vineyard all my life except the last six years," Reiche said in an interview. "Most of the people opposing me strongly oppose public financing and they would genuinely like someone who is unalterably opposed.

"While I have great reservations and objections in a practical sense [about public financing of congressional races], in the philosophical sense I have honestly not made up my mind. I have to be honest with them."

Reiche was appointed to replace Vernon W. Thomson, the former Republician congressman from Wisconsin, whose name was not resubmitted by the Republican leadership. Humphrey (along with Thomson) would like to see Thomson remain for aother six-year term, a factor that further complicates the dispute.

The nomination last year of Republican Sam Zagoria to the FEC also produced a prolonged controversy because his name was not submitted by the Republican leadership. President Carter eventually withdrew the Zagoria nomination and agreedto abide by the Republican list.