Sen. Lisa Murkowski likely faces a cool but respectful reception when she returns to Washington, D.C., next week: She probably won’t be barred from the Republican Conference’s lunches or other events, but her GOP colleagues will make no bones about working to ensure her defeat in November.

Murkowski’s decision to run for re-election as a write-in candidate after losing Alaska’s GOP primary to Joe Miller frustrated Senate Republican leaders and party strategists, who believe she has increased the odds that Democratic nominee Scott McAdams will slide to victory in November and capture a presumably safe GOP seat for the Democrats.

But a GOP leadership aide said Senate traditions will trump any anger when she returns to the chamber.

“It will be respectful. It is the Senate, after all,” the leadership aide said.

A senior GOP aide acknowledged that Murkowski would be treated cordially — although she should expect her colleagues to actively work against her campaign.

“Sen. Murkowski will be treated just like any sitting Senator, but it will be very clear that she does not have Republican support in her re-election. We respect the wishes of the primary voters and believe she should as well,” the senior aide said.

Republican aides said that while the Conference’s weekly lunches are often used to map out message strategies that play into the campaigns, leaders are not expected to bar Murkowski from attending them.

“I suspect it won’t be an issue,” the GOP leadership aide agreed.

Minority Leader Mitch McConnell (Ky.) probably will not hold an election to fill Murkowski’s position as vice chairwoman of the Republican Conference until after the November election. Murkowski resigned her leadership position just before announcing her write-in campaign.

According to a GOP leadership source, the vice chairman slot will remain vacant until the November lame-duck session, when the Conference will vote on all party leadership slots. Sen. John Barrasso (Wyo.) has already indicated he will run for Murkowski’s position, and Sen. Tom Coburn (Okla.) has endorsed him.

Another leadership aide indicated it is unlikely McConnell will move to strip Murkowski of her various committee seats.