Story highlights McConnell said they'd strike a deal to avoid shutdown

He said proposals like Trump's wall would be negotiated

Washington (CNN) Senate Majority Leader Mitch McConnell said Sunday he is "very confident" Congress will avoid government shutdown when the current government spending law expires in late April.

Asked by Chris Wallace on "Fox News Sunday" if he would be prepared to risk a government shutdown over GOP agenda items like President Donald Trump's proposed border wall or defunding Planned Parenthood, McConnell said, "We're going to negotiate all of those items in the context of this funding bill."

When pressed, the Kentucky Republican declined to say he'd be willing to risk a government shutdown over the wall, but also argued that Senate Democrats -- not Trump -- would likely take the heat for any potential shutdown.

"I would advise President Trump: 'Don't worry about them sticking that label on you. Congress owns the government shutdown brand,'" McConnell said. "There's no incentive, frankly, for either side to go to the brink."

The Republican Party's slim majority in the Senate means it will need support from at least a few Democrats in order to pass a funding measure. McConnell said the process was going forward "on a bipartisan basis" so far and would continue to include input from Democrats and Trump's administration.

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