President Barack Obama drove to Capitol Hill on Tuesday for meetings with House and Senate Republicans, but his bipartisan outreach appeared to hit a speed bump. Still, the reason may have more to do with philosophical differences than partisan politics or “the old ways of Washington.”

Republican sources insisted that while GOP Members genuinely appreciated Obama’s gesture in meeting with them in the Capitol, they are unable to back stimulus legislation they consider too expensive, no matter how nice the president is.

“It’s like asking a lion to be a vegetarian,” one senior Republican aide said. “This party and this group of people are highly skeptical of massive, massive government programs and spending.”

Despite the policy spat, both sides said the courtship would continue.

Republicans said during the meeting with Obama that their door would continue to be open and that they hoped the president would come back. White House officials said they were gratified by the GOP’s appreciation and that Obama will be back.

But there were also signs of irritation. In remarks after the House meeting — a similar session was held with GOP Senators — Obama said Republicans “may just not be as familiar with what’s in the package as I would like” and that while he doesn’t expect every Republican to support it, “I do hope that we can all put politics aside and do the American people’s business right now.”

White House Press Secretary Robert Gibbs in his daily briefing twice noted that Republican leaders had urged their Conference to oppose the measure even before Obama arrived on Capitol Hill.

One top GOP aide said the House leadership’s hand was forced because the rule for debating the stimulus bill on the House floor was going to be voted during the day. “It might have been a little better if the meeting was last week,” he said.

Republicans said that despite whiffing on moving Republicans toward the bill, Obama’s appearance generated significant goodwill. House Republican Conference Chairman Mike Pence (Ind.) ended the session by thanking Obama for his outreach, one source in the room said.

And Members expressed their appreciation afterward.

“The president was enormously charming, really built a good rapport with Members, and I think would do well to show up quite often,” said Rep. Mark Kirk (R-Ill.), a co-chairman of the moderate Tuesday Group. “Unfortunately, I don’t think he swung a single vote in the room.”

Kirk said he hoped that Obama didn’t come away from the meeting giving up on reaching out to Republicans. “That would be a mistake because a number of Members dramatically improved their impression and opinion of him across the board, even though they are probably going to vote against [the bill] tomorrow.”

But Democrats were skeptical and warned that the GOP would cross the hugely popular Obama at their own peril.

Rep. Lynn Woolsey (D-Calif.), chairwoman of the Progressive Caucus, had predicted that all of the overtures to Republicans wouldn’t amount to much.

“I see this as a learning experience for our president, and a lot of us aren’t surprised at all,” Woolsey said. “I’d feel duped if I didn’t expect it.”

Woolsey said liberals were willing to give Obama some room to try to get Republicans on board but are less likely to do so in the future based on the way the stimulus bill has worked out.

Rep. Alcee Hastings (D-Fla.) said it would hurt Republicans to be seen rejecting Obama’s overtures. “They can’t say that he didn’t come and discuss it with them,” he said. “They need to be very careful.”

Republicans assert their problem is with the Democratic leadership and not Obama, charging that Democrats have excluded them from the legislative process — a charge the Democrats deny.

Though Obama did not specifically respond to GOP concerns about House Democratic leaders, many left the meeting with the impression that he will try to correct some of what they view as problems in the stimulus bill as it wends its way through the legislative process. During the session, sources said, Obama appeared solicitous of their concerns and noted that the House bill that will be voted on this week is not final.

Republicans were particularly outraged, sources said, when Speaker Nancy Pelosi (D-Calif.) asserted on a Sunday talk show that a family-planning provision in the bill would save money. Obama called Energy and Commerce Chairman Henry Waxman (D-Calif.) on Monday and asked that the provision be removed, the White House confirmed.

One top House Republican aide noted that Democrats had little incentive to heed Obama’s bipartisan call and please the GOP, at least this early in the process. Since the bill will be changed, they have reason to try to make the initial version as favorable to them as possible in order to have leverage with the Senate — just like the House GOP did when it was in charge.

“Even when things change, they don’t change,” he remarked.

A session that followed with Republican Senators also appeared unlikely to guarantee Obama much support for the stimulus, but the conversation was less focused on the stimulus than the House meeting, covering subjects such as the upcoming debate on a second batch of Troubled Assets Relief Program bailout money.

Steven T. Dennis and Jackie Kucinich contributed to this report.