Updated at 4:39 p.m.

TAMPA -- Grassroots Republican activists and Ron Paul supporters came up shy in their effort to beat back two major rule changes Tuesday at the Republican National Convention.

Amidst a contentious scene on the floor of the convention, House Speaker John Boehner (R-Ohio) ruled that the committee rules had passed by a voice vote -- despite loud protest from many in the arena.

Delegates -- many of them from the Texas delegation, where Paul serves in Congress -- booed loudly after Boehner made the ruling and chanted "point of order" in an attempt to order a re-vote.

Soon, though, the fervor died down, and the business of the convention proceeded.

Grassroots activists and Paul supporters were fighting against rules that would require states to allocate delegates according to the statewide vote and would allow the RNC to change its rules without a full convention vote. Both, they said, would dilute the influence of grassroots activists.

From that point on, the delegates were largely respective of Boehner and other speakers.

Prior to the rules vote, there was also a contentious vote on the report from the committee's credentials committee, which prevented half the delegates from Maine -- many of them Paul supporters -- from being seated after ruling that there were problems with their selections.

The credentials report also passed by voice vote, prompting chants of "Seat Maine now" from Paul supporters in the crowd. At one point, RNC Chairman Reince Priebus had to gavel them back into order as the chanted over the next speaker.

Prior to the floor votes, the Republican National Committee rules committee Tuesday afternoon formally adopted its proposed rules after striking a deal with Texas Republicans and Paul supporters and backing off a rule that would have given a presidential candidate the power to disavow a delegate from a given state. But with the rules set to go before a vote of the full convention, Paul supporters and grassroots activists were feverishly gathering signatures to fight other rules changes on the floor.

That effort fell short, as organizers quickly voted on the committee reports on the floor.

The RNC rules committee last week adopted a rule under which states would be required to allocate delegates according to the statewide vote -- a move that was pretty clearly aimed at avoiding situation like this year, when Ron Paul supporters effectively took over the delegate-nominating process in a few states that he didn't win. Some states, like Maine, currently do not allocate delegates based on the statewide vote, but rather through a lengthy and complicated process that follows.

In addition, the rules committee adopted another rule that would allow for the committee to changes its rules between conventions. Currently, a full convention vote is needed to change the rules.

Paul supporters and grassroots activists said Monday afternoon that they would fight both rules, arguing that they undercut the grassroots. In order to raise their objections on the floor, they needed to gather signatures from 25 percent of members of the rules committee, which they were feverishly doing after the formal rules committee meeting Tuesday.

"We're going to fight it on the floor," said Dudley Brown, a rules committee member and unpledged delegate from Colorado. "Everybody in this room knows -- and (Romney adviser John Sununu) clearly said -- there are members whose phones are ringing off the hook."

Things got heated after the rules committee meeting. Brown even accused another rules committee member of grabbing documents seeking a floor fight from a woman passing them around and refusing to give them back.

"I don't like men pushing around women," Brown said.

The movement isn't just a Ron Paul thing; grassroots and tea party Republicans have also joined the cause. Sarah Palin has made her support for the floor fight known, and Rep. Michele Bachmann (R-Minn.) said after the rules committee meeting that she also supports the so-called "minority report" -- the technical term for the opposition's effort to bring the issue to the floor.

"I've been for the minority report, because the backbone of our party is the grassroots,"  Bachmann said after noting the Minnesota support for the opposition. (Minnesota is one of a few states where Ron Paul supporters took over the delegate-selection process.

Another RNC committee last week recommended that half the Maine delegation not be seated after it found problems with the way the state's delegates were selected.

As delegates were taking to the floor Tuesday, Paul supporters in the crowd were chanting, "Seat Maine now."

“It’s a railroad. They’re trying to stage a coup and make the grassroots completely irrelevant for the future,” said alternate delegate and Paul supporter Jeremy Blosser, 36, of Fort Worth, Tex., wearing his delegation’s white cowboy hat as he waited for the opening gavel early Tuesday afternoon. A lot of people, he said, “are upset about these credentials shenanigans.”

Darrell Johnson, an alternate delegate from Michigan, said he’d heard rumors that some delegates will turn their back on Mitt Romney when he speaks.

"We're fighting for our brothers and sisters of Maine. We sat here and objected," said Harrison Whitaker, a delegate from Texas who said he would vote for Romney but supports Paul. "We don't want to see people get cheated. Stuff like this, it's so disheartening."

Maine is one of a few states where Paul supporters effectively took over the delegate-selection process, even though he didn't carry the popular vote in the state. The new RNC rules would prevent that from happening in the future.

The RNC rules committee and grassroots activists were able to come together on one issue.

Texas Republicans led the fight, initially taken up by Paul supporters, against a rule that would allow a candidate to disavow individual delegates. They said it could pave the way for the candidate to stack the delegate ranks with wealthy donors rather than party activists.

In a letter released late Monday, Indiana Republican National Committeeman Jim Bopp and other RNC members instead proposed a new penalty for delegates who cast a vote for a candidate other than the one they are bound to vote for. The rule was adopted by the committee Tuesday.

"The resolution that we have reached is straightforward," wrote Bopp and other top RNC officials, including Henry Barbour, Ron Kaufman and John Ryder. "It simply prevents a bound delegate from nominating or casting a vote for a different presidential candidate than the one to whom the delegate was legally bound by state law or state party rule."

Joel Achenbach and Philip Rucker contributed to this report.