The $1.2 trillion infrastructure bill, passed Tuesday by the U.S. Senate faces "difficult sledding" among progressive Democrats and Republicans in the House of Representatives.

"If this were a pure infrastructure bill and paid for, no question, I think the bulk of Republicans would support it, including me, it's not," Representative Kevin Brady (R-Tex.) told Yahoo Finance Live.

The bipartisan infrastructure plan proposes spending roughly $550 billion over five years in new money on roads, bridges, waterways, public transit, railways, the power grid and broadband internet. President Biden said, "We can still come together to do big things, important things, for the American people," highlighting the compromise senators from both political parties made to draft and pass the legislation which totals $1.2 trillion in overall spending.

"Getting Republicans involved in these conversations made this bill considerably better compared to the president's original infrastructure bill," Brady said.

But progressive Democrats like Representative Alexandria Ocasio-Cortez (D-NY) said they won't vote for it in the House unless the Senate passes a second $3.5 trillion spending plan via budget reconciliation.

"Just because something is bipartisan doesn't mean it's good," said Ocasio-Cortez last week. "Look at Wall Street bailouts."

'Rising prices are continuing to be a huge problem'

House Speaker Nancy Pelosi plans to tie the infrastructure vote to passage of the $3.5 trillion reconciliation plan in the Senate. Brady said that spells trouble. "So I don't know if the very radical left, will push her into what you and I think is a more egregious bill, tied to these big tax and spending, reconciliation," he said. "I don't know, she's got a big problem on her hands."

Brady said infrastructure "done right" can help with economic growth. But he warns injecting $1 trillion in government spending via infrastructure, "when rising prices are continuing to be a huge problem" and contemplating another $3.5 trillion on top of it will ignite inflation "not just for the short term, but for an extended period, and no one wants to see that," he said.

Inflation expectations are starting to take hold among Brady's constituents, he said. "And that's what worries me because as you know, once those inflation expectations, you know, take hold, then you've got big problems going forward."