Washington (CNN) Congressional Republicans are trying to do everything President-elect Donald Trump wants -- and that they've promised voters they'd do -- without blowing up the federal budget.

According to Sen. Rand Paul, it's not working.

Paul, the Kentucky Republican, is leading a lonely charge against GOP leaders' plan to approve a budget resolution that clears the way for Obamacare's repeal -- in part by lifting spending limits in a way he says would balloon the deficit by $9.7 trillion over 10 years.

He met with 25 House Republicans on Thursday -- mostly members of the conservative Freedom Caucus -- to urge them to stymie the measure in the House after he was the lone Republican to oppose it in the Senate.

Paul complained on a call with reporters Thursday evening that Republicans are doing exactly what they accused President Barack Obama and Democrats of doing for years: Spending recklessly to accomplish political objectives.

"I think it's important, no matter who's in charge ... to be vigilant for conservative principles," Paul said. "Before I got in politics, I was a private citizen and I watched the George W. Bush administration -- with Republicans complicit and Democrats complicit -- grow the debt from $5 to $10 trillion. The Obama administration grew it from $10 to $20 trillion."

House and Senate leaders have said the budget resolution is merely a stopgap designed to allow them to strike down Obamacare without Democratic votes in the Senate, and say it won't take effect and actually increase spending.

But Paul said he fears Republicans will use the same claims later this year to enact Trump priorities including tax reform.

If Paul is ultimately successful, it would thwart the avenue Republican leaders had identified to work around Democratic objections and roll back Obama's signature domestic achievement.

It's not the only area where deficit spending concerns are causing at least some Republicans to hit the brakes on Trump's priorities.

A massive infrastructure initiative was a big talking point for the President-elect, but House Transportation Committee Chairman Bill Shuster , R-Pennsylvania, said not to expect plan details any time soon. Right now, he says the focus will be figuring out how to pay for the trillion-dollar price tag.

"We're going to start to work on it, but first of all, you've got to figure out the pay for it, which will come, I believe, in the first 100 days. Then in the next second 100 days is when we'll put together a big infrastructure package," he said.

While Paul cast the lone vote against the budget measure Wednesday, other Senate Republicans raised concerns.

Sens. Marco Rubio, Ted Cruz and Mike Lee sent a letter to the party's Senate leaders urging "transparent spending and revenue numbers" to be included in the budget resolution for 2018 -- even as they agreed with the 2017 budget resolution that includes the language that will help the GOP repeal Obamacare.

"Our votes in favor of the 'Obamacare Repeal Resolution' do not indicate in any way our support for the revenue, spending and deficit numbers therein, nor for the use of those numbers as the basis for future federal budgets," the three wrote.

Paul, meanwhile, didn't leave his meeting with the House Republicans with any firm commitments, as Freedom Caucus members said they'd discuss the topic at a caucus meeting Monday.

"The Freedom Caucus has been very strong in its support of a balanced budget, and it's too early to tell whether that would be a casualty of voting for this budget," said Rep. Mark Meadows, the chairman of the House Freedom Caucus.

"Any time you look at anything, you've got to be concerned about the cost," Meadows said.

Rep. Jim Jordan, R-Ohio, said "we're waiting for our meeting" to discuss the group's position.

"We heard some good information from Rand. We had some good dialogue back and forth," he said.

Others deflected questions about the mechanics of how Congress will roll back Obama's health law.

"I'm supportive of repealing Obamacare," said Rep. Justin Amash, R-Michigan.

Paul acknowledged in an interview with CNN Wednesday that the Senate GOP budget move is related to Obamacare but says it doesn't have to raise the deficit.

"We're told they're doing this just so they can get rid of Obamacare, and that's true. Well we could have done both. We could have introduced a budget that actually leads to balance, is fiscally conservative and repeals Obamacare," Paul said.