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I don’t know anyone who is more in touch with his constituency than Mitch McConnell, said Jack Richardson of Louisville, party chairman in Jefferson County, the state’s most populous county and home to Mr. McConnell.

Mr. McConnell recently acknowledged grass-roots discontent over immigration.

During the immigration debate, and ever since, countless well-informed Americans spoke up about the need to enforce our borders and our laws, he said. Their voice was heard in the Capitol and the White House. The billions we’ve added to the homeland security funding bill for border security and interior enforcement, and the administration’s enhanced commitment to cracking down on illegal immigration are necessary steps toward securing our nation — and living up to the expectations of our constituents.

Another McConnell supporter, Bourbon County Chairman Andre Regard, said, I would be surprised if McConnell faces a challenge because of immigration. I think we should give everyone amnesty and start over.

Other party leaders in the state privately made it clear that supporting Mr. McConnell is important because of the benefits he brings Kentucky through his seniority — he is completing his fourth term — and as the Republican leader in the Senate.

Ballard County party Chairman Charley Martin said: I know immigration is a very emotional issue with Republicans, but it’s not the fundamental issue. The party wants to continue the conservative views of Senator McConnell — the views he stood for through the years.