Republicans from Washington, D.C., to Chicago are frustrated with Rep. Mark Kirk — their likely 2010 Senate nominee — because of the way he handled a potential primary challenge last week from the state party chairman.

Few, if any, Republicans with state and national ties were willing to go on the record with their criticism of Kirk, who avoided a primary with state GOP Chairman Andy McKenna after the two men discussed the Senate race over the weekend and McKenna agreed to step aside.

“I know the National Republican Senatorial Committee is very frustrated with Mark Kirk because he was being indecisive,— said a Republican source familiar with the situation.

An Illinois GOP operative who was inclined to support McKenna said Kirk’s rollout raised eyebrows and didn’t help to breed confidence in the five-term Congressman from suburban Chicago.

“The other story coming out of this is the mismanagement of Mark’s rollout,— the Republican said. “The NRSC is in a bind because this was a recruitment victory for them. They were saying all along that Mark Kirk was who they wanted.—

Kirk has yet to officially announce that he will run for Senate, nor has he filed any paperwork with the Federal Election Commission. But he said in a statement Monday that he will announce his intentions about running for statewide office soon.

A source close to the Kirk campaign maintained that the Congressman was just waiting for the Democratic field to shake out before he made the final call about running.

“From the beginning, Kirk had made it clear that he was waiting for the Democratic field to shape up, and he always agreed with the Illinois chairman that there shouldn’t be a contentious primary,— the source said. “He’s currently making calls to hundreds of Illinois Republicans, including elected officials.—

McKenna, GOP leaders and Illinois donors had been pressuring Kirk for months to make a decision about the race. McKenna, who also sought the GOP nomination for the same Senate seat in 2004, told Kirk he was moving forward with his own bid.

Kirk was waiting to see if Attorney General Lisa Madigan, the most popular elected Democrat in Illinois, was going to run. But when Madigan announced last week that she was going to run for re-election, Kirk immediately expressed to the NRSC his intention to run for Senate.

McKenna was meeting with the NRSC and other officials in Washington in an effort to move forward with his own bid. The Illinois party chairman had gone as far as to work with political consultants on his bid and refused to defer to Kirk to run for Senate until last weekend.

“Andy was really committed to making sure there was a qualified candidate in this race from the get-go,— said an Illinois Republican who was inclined to support McKenna. “There was a lot of indecisiveness on Mark’s part.—

One county chairman from a rural part of the state requested a conference call with all of the state’s GOP county chairmen and the Congressman on Thursday. According to sources familiar with the conference call, numerous county chairmen throughout the state said they did not want to see Kirk run because of his vote for cap-and-trade legislation.

“I was not on the call, but my understanding was that it not go well,— an Illinois Republican said.

The Illinois delegation was also upset about his cap-and-trade vote and took the weekend to mull over the potential candidates. After all, Rep. John Shimkus (Ill.) was one of the leading Republicans railing against the legislation.

By Friday morning, Kirk was making calls to tell people that he was leaning against a run — but he told Roll Call on Friday afternoon that he was going to continue to discuss the matter with McKenna over the weekend.

McKenna released a statement Monday that said he told Kirk he would not oppose him in the Senate primary.

According to two sources close to the delegation, Illinois Members will likely follow Rep. Judy Biggert (R) and line up in support behind Kirk. Biggert told a local newspaper last week that she is supporting Kirk.

“The good thing about the Illinois delegation is they are able to solve their problems internally and everybody wants to win,— a source close to the delegation said. “We have a problem. We made an agreement. Now everybody wants to win.—

Democrats will most likely not avoid a primary of their own for the seat formerly held by President Barack Obama.

State Treasurer Alexi Giannoulias announced his exploratory committee for the seat early this year and so far remains the only viable Democratic candidate in the race. According to his campaign, Giannoulias plans to announce his final decision about the race later this month, but there’s little doubt that he’s gunning hard for the seat.

Giannoulias has raised $1.8 million so far, including about $670,000 in the second quarter. And in the wake of last week’s Republican primary turmoil, he released a list of endorsements from more than 60 local officials — including two Members of Congress.

Illinois Democratic Reps. Phil Hare and Bill Foster announced Monday they were backing Giannoulias. Hare Communications Director Tim Schlittner said in a statement that they support Giannoulias because he would provide “bold, fresh leadership— for Illinois.

“Congressman Hare has been thoroughly impressed by Mr. Giannoulias’ enthusiasm, work ethic, grasp of the issues, and outreach to downstate Illinois,— Schlittner said. “They worked hand in hand to save thousands of Illinois jobs at Hart Schaffner Marx.—

Chicago Urban League President Cheryle Jackson has also opened an exploratory bid, but many Democrats believe her tenure as spokeswoman for disgraced ex-Gov. Rod Blagojevich (D) could be damaging to her candidacy. Nonetheless, she might rally much of the the African-American vote in the Chicago area now that Sen. Roland Burris (D) has announced that he will not run in 2010.

Businessman Chris Kennedy is also expected to run for the Democratic nod, although the son of the late Sen. Robert F. Kennedy (D-N.Y.) is beginning to take heat for taking his time to announce a campaign. A local policeman has filed a complaint with the FEC charging that Kennedy has spent more than $5,000 on his yet-to-be-announced campaign, a threshold which would require him to file paperwork with the FEC.