Sen. Chuck Grassley
Charles (Chuck) Ernest GrassleyThe Senate's grown-ups in the Trump-Russia probe follow facts, not politics Trump: 'No final straw' on Pruitt GOP lawmakers relieved with Pruitt’s departure MORE (R-Iowa) said his committee will take up legislation to protect special counsel Robert Mueller
Robert Swan MuellerSasse: US should applaud choice of Mueller to lead Russia probe MORE despite opposition from Senate Majority Leader Mitch McConnell
Addison (Mitch) Mitchell McConnellGraham: Trump's Supreme Court picks 'all winners' Trump says he's close to making final Supreme Court decision An end game on Supreme Court nominations MORE (R-Ky.).
"They got together, so I feel an obligation to keep my word and move forward," Grassley said when asked if he would still give the special counsel legislation a vote.
Grassley had previously urged supporters of two competing special counsel bills to strike an agreement and merge their proposals.
That legislation is on the agenda for a committee business meeting on Thursday, but an actual vote is expected to be delayed until next week.
McConnell said he has no intention of bringing the bill up for a floor vote during an interview with Fox News on Tuesday.
"I'm the one who decides what we take to the floor, that's my responsibility as the majority leader, and we will not be having this on the floor of the Senate," he told Fox News.
McConnell has argued for months that he doesn't believe legislation protecting the special counsel is necessary. He has said he doesn't believe President Trump
Grassley sidestepped a question about whether he would urge McConnell to bring up the bill, noting it still needs to get out of committee. He said McConnell has a "terrible job."
"But I can't worry about what's going on on the floor. I've just got to do what I can do," he said.
With at least GOP Sens. Thom Tillis
But it faces an uphill climb to getting 60 votes in the Senate, much less passing the more conservative House.
A bipartisan group of senators introduced legislation last week that would codify that only a senior Justice Department official can fire a special counsel and give Mueller or any other special counsel an "expedited review" of any firing.
If a court determines a special counsel wasn't fired for "good cause," the person would be reinstated.