(CNN)Top Senate Republicans are not embracing the assertion by a top White House adviser that President Donald Trump wants Congress to approve another $2 trillion worth of stimulus to help bolster the economy.

       Walking off the floor, CNN asked Senate Majority Leader Mitch McConnell if he could back a $2 trillion plan as White House trade adviser Peter Navarro said Trump is seeking in the next round of stimulus.

       "Well, as I've already said, we'll be looking in July to make a decision about whether to go forward with another rescue package," McConnell, a Kentucky Republican, said Monday. "And we'll let you know."

       McConnell didn't respond to a question when asked if he's concerned such a price tag could grow the deficit.

       Asked about the $2 trillion price tag, Senate Finance Chairman Chuck Grassley said Monday that senators still need to assess how the existing stimulus dollars -- nearly $3 trillion worth -- have been spent to determine what additional legislation is needed. Grassley said there are still outstanding questions about how the economy has been impacted by Covid-19, how $150 billion already given to states and localities is being spent and how health care money has been handled.

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       "By the way, there's going to be some bill next time," said Grassley, an Iowa Republican. "There's no doubt about that as far as I can tell."

       Asked if he backs a payroll tax cut as Trump has sought, Grassley said: "It seems to me -- if it's just til the end of the year, I don't know whether it will do the good."

       Grassley said Congress needs to "spend greater time" to "transitioning people" who may soon see their enhanced unemployment benefits dry up.

       On Saturday, Navarro said Trump wants a new package of "at least $2 trillion dollars that is strategically focused around the President's two simple rules -- Buy American, Hire American -- along with incentives for American companies to bring offshored jobs back home."

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