Call it just the latest “Byrd Rule.”

In an apparently unprecedented move, the Senate Budget Committee will allow proxy voting during today’s markup of the budget resolution in deference to Sen. Robert Byrd (D-W.Va.), who was readmitted to a local hospital on Wednesday afternoon.

The Senate agreed on Tuesday to a unanimous consent request for a one-day rule allowing proxy voting in the budget panel on behalf of the chamber’s senior Senator, overturning a tradition of forbidding proxies on budget votes.

Byrd’s office said on Wednesday that the 90-year-old Senator was readmitted after a reaction to antibiotics he is taking to treat a urinary tract infection, and the stay is expected to be brief.

A Byrd spokesman defended the exception.

“This was done as a precautionary measure in the event that Sen. Byrd is unable to attend markup of the [fiscal] 2009 budget resolution,” said Byrd spokesman Jesse Jacobs, who noted it was “a one-time, one-day change.”

Senate Budget Chairman Kent Conrad (D-N.D.) said he sought to have Byrd temporarily replaced on the panel but was overruled by Majority Leader Harry Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.), who worked out the deal.

“I favored having another Senator put on temporarily,” Conrad said. But he said the decision was made not to replace Byrd because the new Senator would have no chance to get up to speed on the budget.

“I’ve always been opposed to proxy voting,” he added. Conrad said the budget panel’s unique status justifies the rule against proxies.

“We’re the only committee that can report on a fast-track basis to the floor,” he said. “That’s why there is the rule.”

Sen. Judd Gregg (R-N.H.), the ranking member, said it is reasonable to allow proxies when a Member is ill, though he agreed with Conrad that it should not be a regular practice.

“I said, ‘Fine, make it just this markup,’” Gregg said. He added that there was some thought that Byrd would be able to make the markup, so they wanted to avoid taking him off the committee.

“As a practical matter, it’s not going to affect the outcome,” Gregg said, because Democrats could always have replaced Byrd and maintained their 12-11 margin on the committee.

Some Republicans recalled that in 2003, they were faced with a nearly identical circumstance.

When Sen. Pete Domenici (R-N.M.) fell ill before the markup, then-Chairman Don Nickles (R-Okla.) asked Conrad for permission to allow proxy votes, but Conrad refused, according to a former Senate Republican budget staffer.

Then in 2004, the staffer said, one of Conrad’s own — Sen. Tim Johnson (D-S.D.) —was also unable to make the markup because of illness. Nickles offered to allow Johnson to vote by proxy, but Conrad again declined to change the panel’s rule, the staffer said. Asked about those incidents, Conrad noted that he has been consistent in his opposition to proxies for either party.