UPDATED 03/14/12 7:32 a.m.

WASHINGTON (CBS) — There is word that U.S. Sen. Mark Kirk (R-Ill.) is recovering well as he battles back from his stroke.

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As WBBM Newsradio’s Regine Schlesinger reports, Kirk’s Congressional colleague, U.S. Rep. John Shimkus (R-Ill.) met with Kirk Sunday night. In a column quoted by the Chicago Sun-Times’ Lynn Sweet, Shimkus writes that Kirk is “coming back.”

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The Sun-Times quotes Shimkus as saying that mentally, Kirk is sharp, and already would be capable of casting “knowledgeable votes.” At the same time, Shimkus says Kirk told him “that nothing he has done has been as difficult as this road to recovery,” the Sun-Times reported.

But Kirk’s office emphasizes that he cannot cast votes again until he returns to Washington.

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Kirk spends every day at the Rehabilitation Institute of Chicago, where he pushes through a grueling physical therapy regimen, uses a treadmill, and walks the hallways, the Sun-Times reported.

Shimkus described his Sunday night visit with Kirk in the column.

“Mark was sitting up with a smile on his face,” Shimkus wrote. “His short hair reminded me of Sgt. Carter from the TV show Gomer Pyle, USMC.”

Kirk had the stroke the weekend of Jan. 21 and has undergone a series of surgeries, including an operation a few weeks ago to reattach part of his skull that had been removed to alleviate brain swelling. Doctors initially said the senator lost some physical abilities on the left side of his body.

Physicians have said Kirk suffered an ischemic stroke, the most common type. According to the American Stroke Association’s website, ischemic strokes are the most common form of stroke, accounting for about 87 percent of all cases. They are the result of an obstruction within a blood vessel that supplies blood to the brain, caused by fatty deposits in the blood vessels.

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Kirk, a North Shore Republican, was elected to the U.S. Senate in 2010, winning the seat once held by President Barack Obama. Before that, he spent 10 years in the U.S. House.