A leading Tea Party senator said Wednesday he would vote down the House-passed spending bill that cuts $61 billion from the budget if it comes to a vote in the Senate.

Sen. Rand PaulRandal (Rand) Howard PaulMcConnell in tough position as House eyes earmark return Rand Paul says Fauci owes parents and students an apology over pandemic measures Grassley returns to Capitol after having coronavirus MORE (R-Ky.) said that House Republicans' measure funding the government through the rest of the year doesn't make deep enough cuts, and for that reason, he would vote against it.

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"Yeah, you have to do much more. You're not even close," Paul said on ABC's "Good Morning America" when asked if he'd vote against both the short-term and long-term funding measures in their current form.

"Neither plan is sustainable. So what I'm about, and what the Tea Party's about, is keeping both Republicans and Democrats honest about this," Paul said. "You have to cut enormous amounts; you have to do much more than what anybody has proposed."

Paul's threat could complicate the already tricky math in Congress over how to prevent a government shutdown in the coming weeks.

The government runs out of money on March 4, and faces a shutdown barring congressional action. The GOP House passed a continuing resolution (CR) that funds the government at reduced levels the rest of this fiscal year. But that bill, which cuts $61 billion from already-allotted spending, is all but dead on arrival in the Senate, and President Obama has threatened to veto it.

That leaves the House and Senate with the option of passing a short-term extension in funding, but they're already sparring over that. House GOP leaders have said a short-term CR would still have to cut spending, while Senate Democratic leaders insist on an extension at current spending levels. Both sides spent the better part of Tuesday accusing the other of negotiating in bad faith and rooting for a government shutdown for their own political benefit.

Even if a deal is cut to avoid a shutdown, it could be complicated by Paul and other senators, who could conceivably go further than just voting against any plan, and filibuster it, meaning that 60 votes would be necessary to break the logjam.

All but three House Republicans voted for the long-term continuing resolution in the House. Those who didn't also said it didn't cut deeply enough.